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Principle: Compound angle: sin/cos/tan(A ± B)
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Q1
#1
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
cot
α
\cot\alpha
cot
α
and
cot
β
\cot\beta
cot
β
are the roots of the equation
x
2
+
b
x
+
c
=
0
x^2 + bx + c = 0
x
2
+
b
x
+
c
=
0
with
b
≠
0
b \neq 0
b
=
0
, then the value of
cot
(
α
+
β
)
\cot(\alpha+\beta)
cot
(
α
+
β
)
is
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
c
−
1
b
\dfrac{c-1}{b}
b
c
−
1
B
1
−
c
b
\dfrac{1-c}{b}
b
1
−
c
C
b
c
−
1
\dfrac{b}{c-1}
c
−
1
b
D
b
1
−
c
\dfrac{b}{1-c}
1
−
c
b
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[Q15 · Apr · 2017]
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Q2
#2
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Hard
If
sin
θ
=
3
sin
(
θ
+
2
α
)
\sin\theta = 3\sin(\theta+2\alpha)
sin
θ
=
3
sin
(
θ
+
2
α
)
, then the value of
tan
(
θ
+
α
)
+
2
tan
α
\tan(\theta+\alpha)+2\tan\alpha
tan
(
θ
+
α
)
+
2
tan
α
is equal to
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
−
1
-1
−
1
B
0
0
0
C
1
1
1
D
2
2
2
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[Q45 · Apr · 2017]
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Q3
#3
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Hard
The value of
tan
9
°
−
tan
27
°
−
tan
63
°
+
tan
81
°
\tan 9° - \tan 27° - \tan 63° + \tan 81°
tan
9°
−
tan
27°
−
tan
63°
+
tan
81°
is equal to
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
-1
B
0
C
1
D
4
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[Q32 · Sep · 2017]
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Q4
#4
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
What is
sin
105
°
+
cos
105
°
\sin 105° + \cos 105°
sin
105°
+
cos
105°
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
sin
50
°
\sin 50°
sin
50°
B
cos
50
°
\cos 50°
cos
50°
C
1
/
2
1/\sqrt{2}
1/
2
D
0
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[Q38 · Apr · 2018]
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Q5
#5
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
sin
(
x
+
y
)
sin
(
x
−
y
)
=
a
+
b
a
−
b
\frac{\sin(x+y)}{\sin(x-y)} = \frac{a+b}{a-b}
s
i
n
(
x
−
y
)
s
i
n
(
x
+
y
)
=
a
−
b
a
+
b
, then what is
tan
x
tan
y
\frac{\tan x}{\tan y}
t
a
n
y
t
a
n
x
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
a
b
\frac{a}{b}
b
a
B
b
a
\frac{b}{a}
a
b
C
a
+
b
a
−
b
\frac{a+b}{a-b}
a
−
b
a
+
b
D
a
−
b
a
+
b
\frac{a-b}{a+b}
a
+
b
a
−
b
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[Q46 · Apr · 2018]
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Q6
#6
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
cos
α
+
cos
β
+
cos
γ
=
0
\cos\alpha + \cos\beta + \cos\gamma = 0
cos
α
+
cos
β
+
cos
γ
=
0
, where
0
<
α
,
β
,
γ
≤
π
/
2
0 < \alpha, \beta, \gamma \le \pi/2
0
<
α
,
β
,
γ
≤
π
/2
, then what is
sin
α
+
sin
β
+
sin
γ
\sin\alpha + \sin\beta + \sin\gamma
sin
α
+
sin
β
+
sin
γ
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
0
B
3
C
5
2
2
\frac{5\sqrt{2}}{2}
2
5
2
D
3
2
2
\frac{3\sqrt{2}}{2}
2
3
2
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[Q49 · Apr · 2018]
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Q7
#7
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Hard
If
sec
(
θ
−
α
)
\sec(\theta-\alpha)
sec
(
θ
−
α
)
,
sec
θ
\sec\theta
sec
θ
and
sec
(
θ
+
α
)
\sec(\theta+\alpha)
sec
(
θ
+
α
)
are in AP, where
cos
α
≠
1
\cos\alpha \neq 1
cos
α
=
1
, then what is the value of
sin
2
θ
+
cos
α
\sin^2\theta + \cos\alpha
sin
2
θ
+
cos
α
?
Add
Lever: AP three-term: 2b = a + c
A
0
B
1
C
-1
D
1
2
\frac{1}{2}
2
1
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[Q37 · Sep · 2018]
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Q8
#8
NDA → Mathematics → Trigonometric Equations → Solving Specific Forms — Double-Angle, Product, Logarithmic, and Vieta
·
Moderate
If
cos
α
\cos\alpha
cos
α
and
cos
β
\cos\beta
cos
β
(
0
<
α
<
β
<
π
)
(0 < \alpha < \beta < \pi)
(
0
<
α
<
β
<
π
)
are the roots of the quadratic equation
4
x
2
−
3
=
0
4x^2 - 3 = 0
4
x
2
−
3
=
0
, then what is the value of
sec
α
×
sec
β
\sec\alpha \times \sec\beta
sec
α
×
sec
β
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
−
4
3
-\frac{4}{3}
−
3
4
B
4
3
\frac{4}{3}
3
4
C
3
4
\frac{3}{4}
4
3
D
−
3
4
-\frac{3}{4}
−
4
3
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[Q44 · Sep · 2018]
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Q9
#9
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Hard
What is the value of
sin
34
°
cos
236
°
−
sin
56
°
sin
124
°
cos
28
°
cos
88
°
+
cos
178
°
sin
208
°
\dfrac{\sin 34° \cos 236° - \sin 56° \sin 124°}{\cos 28° \cos 88° + \cos 178° \sin 208°}
cos
28°
cos
88°
+
cos
178°
sin
208°
sin
34°
cos
236°
−
sin
56°
sin
124°
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
−
2
-2
−
2
B
−
1
-1
−
1
C
2
2
2
D
1
1
1
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[Q31 · Apr · 2019]
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Q10
#10
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
tan
54
°
\tan 54°
tan
54°
can be expressed as
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
sin
9
°
+
cos
9
°
sin
9
°
−
cos
9
°
\dfrac{\sin 9° + \cos 9°}{\sin 9° - \cos 9°}
sin
9°
−
cos
9°
sin
9°
+
cos
9°
B
sin
9
°
−
cos
9
°
sin
9
°
+
cos
9
°
\dfrac{\sin 9° - \cos 9°}{\sin 9° + \cos 9°}
sin
9°
+
cos
9°
sin
9°
−
cos
9°
C
cos
9
°
+
sin
9
°
cos
9
°
−
sin
9
°
\dfrac{\cos 9° + \sin 9°}{\cos 9° - \sin 9°}
cos
9°
−
sin
9°
cos
9°
+
sin
9°
D
sin
36
°
cos
36
°
\dfrac{\sin 36°}{\cos 36°}
cos
36°
sin
36°
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[Q32 · Apr · 2019]
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Set · 2 questions
Consider the following for the next 02 (two) items: It is given that
cos
(
θ
−
α
)
=
a
\cos(\theta-\alpha)=a
cos
(
θ
−
α
)
=
a
,
cos
(
θ
−
β
)
=
b
\cos(\theta-\beta)=b
cos
(
θ
−
β
)
=
b
.
Q11
#11
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
What is
cos
(
α
−
β
)
\cos(\alpha-\beta)
cos
(
α
−
β
)
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
a
b
+
1
−
a
2
1
−
b
2
ab + \sqrt{1-a^2}\sqrt{1-b^2}
ab
+
1
−
a
2
1
−
b
2
B
a
b
−
1
−
a
2
1
−
b
2
ab - \sqrt{1-a^2}\sqrt{1-b^2}
ab
−
1
−
a
2
1
−
b
2
C
a
1
−
b
2
−
b
1
−
a
2
a\sqrt{1-b^2} - b\sqrt{1-a^2}
a
1
−
b
2
−
b
1
−
a
2
D
a
1
−
b
2
+
b
1
−
a
2
a\sqrt{1-b^2} + b\sqrt{1-a^2}
a
1
−
b
2
+
b
1
−
a
2
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[Q36 · Apr · 2019]
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Q12
#12
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Hard
What is
sin
2
(
α
−
β
)
+
2
a
b
cos
(
α
−
β
)
\sin^2(\alpha-\beta)+2ab\cos(\alpha-\beta)
sin
2
(
α
−
β
)
+
2
ab
cos
(
α
−
β
)
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
a
2
+
b
2
a^2+b^2
a
2
+
b
2
B
a
2
−
b
2
a^2-b^2
a
2
−
b
2
C
b
2
−
a
2
b^2-a^2
b
2
−
a
2
D
−
(
a
2
+
b
2
)
-(a^2+b^2)
−
(
a
2
+
b
2
)
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[Q37 · Apr · 2019]
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Q13
#13
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Easy
What is the value of
tan
75
°
+
cot
75
°
\tan 75° + \cot 75°
tan
75°
+
cot
75°
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
2
2
2
B
4
4
4
C
2
3
2\sqrt{3}
2
3
D
4
3
4\sqrt{3}
4
3
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[Q43 · Apr · 2019]
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Q14
#14
NDA → Mathematics → Trigonometric Equations → Solving Specific Forms — Double-Angle, Product, Logarithmic, and Vieta
·
Moderate
If the roots of the equation
x
2
+
p
x
+
q
=
0
x^2 + px + q = 0
x
2
+
p
x
+
q
=
0
are
tan
19
°
\tan19°
tan
19°
and
tan
26
°
\tan26°
tan
26°
, then which one of the following is correct?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
q
−
p
=
1
q - p = 1
q
−
p
=
1
B
p
−
q
=
1
p - q = 1
p
−
q
=
1
C
p
+
q
=
2
p + q = 2
p
+
q
=
2
D
p
+
q
=
3
p + q = 3
p
+
q
=
3
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[Q46 · Apr · 2019]
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Q15
#15
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
What is
(
1
+
tan
α
tan
β
)
2
+
(
tan
α
−
tan
β
)
2
−
sec
2
α
sec
2
β
(1+\tan\alpha\tan\beta)^2+(\tan\alpha-\tan\beta)^2-\sec^2\alpha\sec^2\beta
(
1
+
tan
α
tan
β
)
2
+
(
tan
α
−
tan
β
)
2
−
sec
2
α
sec
2
β
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
0
B
1
C
2
D
4
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[Q48 · Apr · 2019]
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Q16
#16
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
sin
θ
+
cos
θ
=
2
cos
θ
\sin\theta+\cos\theta=\sqrt{2}\cos\theta
sin
θ
+
cos
θ
=
2
cos
θ
, then what is
(
cos
θ
−
sin
θ
)
(\cos\theta-\sin\theta)
(
cos
θ
−
sin
θ
)
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
−
2
cos
θ
-\sqrt{2}\cos\theta
−
2
cos
θ
B
−
2
sin
θ
-\sqrt{2}\sin\theta
−
2
sin
θ
C
2
sin
θ
\sqrt{2}\sin\theta
2
sin
θ
D
2
sin
θ
2\sin\theta
2
sin
θ
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[Q96 · Apr · 2019]
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Q17
#17
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
tan
A
−
tan
B
=
x
\tan A - \tan B = x
tan
A
−
tan
B
=
x
and
cot
B
−
cot
A
=
y
\cot B - \cot A = y
cot
B
−
cot
A
=
y
, then what is the value of
cot
(
A
−
B
)
\cot(A - B)
cot
(
A
−
B
)
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
1
x
+
1
y
\dfrac{1}{x} + \dfrac{1}{y}
x
1
+
y
1
B
1
y
−
1
x
\dfrac{1}{y} - \dfrac{1}{x}
y
1
−
x
1
C
x
y
x
+
y
\dfrac{xy}{x+y}
x
+
y
x
y
D
1
+
1
x
y
1 + \dfrac{1}{xy}
1
+
x
y
1
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[Q63 · Sep · 2019]
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Q18
#18
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Easy
If
tan
θ
=
cos
17
°
−
sin
17
°
cos
17
°
+
sin
17
°
\tan\theta=\frac{\cos 17°-\sin 17°}{\cos 17°+\sin 17°}
tan
θ
=
c
o
s
17°
+
s
i
n
17°
c
o
s
17°
−
s
i
n
17°
, then what is the value of
θ
\theta
θ
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
0
°
0°
0°
B
28
°
28°
28°
C
38
°
38°
38°
D
52
°
52°
52°
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[Q23 · Apr · 2020]
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Set · 3 questions
Directions for the following three (03) items: Read the following information and answer the three items that follow: Let
a
sin
2
x
+
b
cos
2
x
=
c
a\sin^2 x + b\cos^2 x = c
a
sin
2
x
+
b
cos
2
x
=
c
;
b
sin
2
y
+
a
cos
2
y
=
d
b\sin^2 y + a\cos^2 y = d
b
sin
2
y
+
a
cos
2
y
=
d
and
p
tan
x
=
q
tan
y
p\tan x = q\tan y
p
tan
x
=
q
tan
y
.
Q19
#19
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
What is
tan
2
x
\tan^2 x
tan
2
x
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
c
−
b
a
−
c
\frac{c-b}{a-c}
a
−
c
c
−
b
B
a
−
c
c
−
b
\frac{a-c}{c-b}
c
−
b
a
−
c
C
c
−
a
c
−
b
\frac{c-a}{c-b}
c
−
b
c
−
a
D
c
−
b
c
−
a
\frac{c-b}{c-a}
c
−
a
c
−
b
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[Q31 · Apr · 2020]
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Q20
#20
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
What is
d
−
a
b
−
d
\frac{d-a}{b-d}
b
−
d
d
−
a
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
sin
2
y
\sin^2 y
sin
2
y
B
cos
2
y
\cos^2 y
cos
2
y
C
tan
2
y
\tan^2 y
tan
2
y
D
cot
2
y
\cot^2 y
cot
2
y
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[Q32 · Apr · 2020]
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Q21
#21
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Hard
What is
p
2
q
2
\frac{p^2}{q^2}
q
2
p
2
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
(
b
−
c
)
(
b
−
d
)
(
a
−
d
)
(
a
−
c
)
\frac{(b-c)(b-d)}{(a-d)(a-c)}
(
a
−
d
)
(
a
−
c
)
(
b
−
c
)
(
b
−
d
)
B
(
a
−
d
)
(
c
−
a
)
(
b
−
c
)
(
d
−
b
)
\frac{(a-d)(c-a)}{(b-c)(d-b)}
(
b
−
c
)
(
d
−
b
)
(
a
−
d
)
(
c
−
a
)
C
(
d
−
a
)
(
c
−
a
)
(
b
−
c
)
(
d
−
b
)
\frac{(d-a)(c-a)}{(b-c)(d-b)}
(
b
−
c
)
(
d
−
b
)
(
d
−
a
)
(
c
−
a
)
D
(
b
−
c
)
(
b
−
d
)
(
c
−
a
)
(
a
−
d
)
\frac{(b-c)(b-d)}{(c-a)(a-d)}
(
c
−
a
)
(
a
−
d
)
(
b
−
c
)
(
b
−
d
)
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[Q33 · Apr · 2020]
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Q22
#22
NDA → Mathematics → Trigonometric Equations → Solving Specific Forms — Double-Angle, Product, Logarithmic, and Vieta
·
Moderate
If
cot
α
\cot\alpha
cot
α
and
cot
β
\cot\beta
cot
β
are the roots of the equation
x
2
−
3
x
+
2
=
0
x^2-3x+2=0
x
2
−
3
x
+
2
=
0
, then what is
cot
(
α
+
β
)
\cot(\alpha+\beta)
cot
(
α
+
β
)
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
1
2
\frac{1}{2}
2
1
B
1
3
\frac{1}{3}
3
1
C
2
D
3
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[Q43 · Apr · 2020]
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Q23
#23
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Easy
What is the value of
tan
31
°
tan
33
°
tan
35
°
⋯
tan
57
°
tan
59
°
\tan 31° \tan 33° \tan 35° \cdots \tan 57° \tan 59°
tan
31°
tan
33°
tan
35°
⋯
tan
57°
tan
59°
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
-1
B
0
C
1
D
2
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[Q19 · Apr · 2021]
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Q24
#24
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Easy
What is the value of
(
sin
24
°
+
cos
66
°
)
(
sin
24
°
−
cos
66
°
)
(\sin 24° + \cos 66°)(\sin 24° - \cos 66°)
(
sin
24°
+
cos
66°
)
(
sin
24°
−
cos
66°
)
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
-1
B
0
C
1
D
2
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[Q22 · Apr · 2021]
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Q25
#25
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
What is
(
1
+
cot
θ
−
csc
θ
)
(
1
+
tan
θ
+
sec
θ
)
(1+\cot\theta - \csc\theta)(1+\tan\theta+\sec\theta)
(
1
+
cot
θ
−
csc
θ
)
(
1
+
tan
θ
+
sec
θ
)
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
1
B
2
C
3
D
4
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Show solution
[Q24 · Apr · 2021]
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