Question Bank
Bank
Guides
Notes
NDA
Sign in
Filtered questions
42 questions match
Filters
1
Download
· 42
Filtering by:
Principle: Compound angle: sin/cos/tan(A ± B)
Clear all
Copy link
Q26
#26
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
7
sin
θ
+
24
cos
θ
=
25
7\sin\theta + 24\cos\theta = 25
7
sin
θ
+
24
cos
θ
=
25
, then what is the value of
(
sin
θ
+
cos
θ
)
(\sin\theta + \cos\theta)
(
sin
θ
+
cos
θ
)
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
1
B
26
25
\frac{26}{25}
25
26
C
6
5
\frac{6}{5}
5
6
D
31
25
\frac{31}{25}
25
31
Tap an option to check your answer.
Show solution
[Q27 · Apr · 2021]
Report
Q27
#27
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Easy
If
3
cos
θ
=
4
sin
θ
3\cos\theta = 4\sin\theta
3
cos
θ
=
4
sin
θ
, then what is the value of
tan
(
45
°
+
θ
)
\tan(45°+\theta)
tan
(
45°
+
θ
)
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
10
B
7
C
7
2
\frac{7}{2}
2
7
D
7
4
\frac{7}{4}
4
7
Tap an option to check your answer.
Show solution
[Q30 · Apr · 2021]
Report
Q28
#28
NDA → Mathematics → Trigonometric Equations → Solving Specific Forms — Double-Angle, Product, Logarithmic, and Vieta
·
Moderate
If
sin
θ
\sin\theta
sin
θ
and
cos
θ
\cos\theta
cos
θ
are the roots of the equation
a
x
2
+
b
x
+
c
=
0
ax^{2}+bx+c=0
a
x
2
+
b
x
+
c
=
0
, then which one of the following is correct?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
a
2
+
b
2
−
2
a
c
=
0
a^{2}+b^{2}-2ac=0
a
2
+
b
2
−
2
a
c
=
0
B
−
a
2
+
b
2
+
2
a
c
=
0
-a^{2}+b^{2}+2ac=0
−
a
2
+
b
2
+
2
a
c
=
0
C
a
2
−
b
2
+
2
a
c
=
0
a^{2}-b^{2}+2ac=0
a
2
−
b
2
+
2
a
c
=
0
D
a
2
+
b
2
+
2
a
c
=
0
a^{2}+b^{2}+2ac=0
a
2
+
b
2
+
2
a
c
=
0
Tap an option to check your answer.
Show solution
[Q16 · Sep · 2021]
Report
Q29
#29
NDA → Mathematics → Trigonometric Equations → Simultaneous and Combined Trigonometric Systems
·
Easy
If
sin
(
A
+
B
)
=
1
\sin(A+B)=1
sin
(
A
+
B
)
=
1
and
2
sin
(
A
−
B
)
=
1
2\sin(A-B)=1
2
sin
(
A
−
B
)
=
1
, where
0
<
A
,
B
<
π
2
0<A,B<\frac{\pi}{2}
0
<
A
,
B
<
2
π
, then what is
tan
A
:
tan
B
\tan A:\tan B
tan
A
:
tan
B
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
1
:
2
1:2
1
:
2
B
2
:
1
2:1
2
:
1
C
1
:
3
1:3
1
:
3
D
3
:
1
3:1
3
:
1
Tap an option to check your answer.
Show solution
[Q24 · Sep · 2021]
Report
Q30
#30
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
What is
sin
2
(
π
4
+
θ
)
−
sin
2
(
π
4
−
θ
)
\sin^2\left(\frac{\pi}{4}+\theta\right)-\sin^2\left(\frac{\pi}{4}-\theta\right)
sin
2
(
4
π
+
θ
)
−
sin
2
(
4
π
−
θ
)
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
sin
2
θ
\sin2\theta
sin
2
θ
B
cos
2
θ
\cos2\theta
cos
2
θ
C
2
sin
θ
2\sin\theta
2
sin
θ
D
2
cos
θ
2\cos\theta
2
cos
θ
Tap an option to check your answer.
Show solution
[Q33 · Apr · 2022]
Report
Q31
#31
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
f
(
α
)
=
sec
2
α
−
1
f(\alpha) = \sqrt{\sec^2\alpha - 1}
f
(
α
)
=
sec
2
α
−
1
, then what is
f
(
α
)
+
f
(
β
)
1
−
f
(
α
)
f
(
β
)
\frac{f(\alpha)+f(\beta)}{1-f(\alpha)f(\beta)}
1
−
f
(
α
)
f
(
β
)
f
(
α
)
+
f
(
β
)
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
f
(
α
−
β
)
f(\alpha-\beta)
f
(
α
−
β
)
B
f
(
α
+
β
)
f(\alpha+\beta)
f
(
α
+
β
)
C
f
(
α
)
f
(
β
)
f(\alpha)f(\beta)
f
(
α
)
f
(
β
)
D
f
(
α
β
)
f(\alpha\beta)
f
(
α
β
)
Tap an option to check your answer.
Show solution
[Q82 · Sep · 2022]
Report
Q32
#32
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
α
\alpha
α
and
β
\beta
β
are complementary angles such that
α
−
β
=
π
6
\alpha-\beta=\dfrac{\pi}{6}
α
−
β
=
6
π
and
m
tan
β
=
n
tan
α
m\tan\beta=n\tan\alpha
m
tan
β
=
n
tan
α
, then what is
(
m
+
n
m
−
n
)
\left(\dfrac{m+n}{m-n}\right)
(
m
−
n
m
+
n
)
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
2
B
2
3
\dfrac{2}{\sqrt{3}}
3
2
C
1
D
1
3
\dfrac{1}{\sqrt{3}}
3
1
Tap an option to check your answer.
Show solution
[Q27 · Apr · 2026]
Report
Set · 2 questions
For the following two (02) items: Let
p
=
csc
20
°
p = \csc 20°
p
=
csc
20°
and
q
=
csc
70
°
q = \csc 70°
q
=
csc
70°
.
Q33
#33
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Hard
What is
(
3
p
4
−
q
4
)
\left(\dfrac{\sqrt{3}p}{4}-\dfrac{q}{4}\right)
(
4
3
p
−
4
q
)
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
-1
B
0
C
1
D
2
Tap an option to check your answer.
Show solution
[Q27 · Sep · 2025]
Report
Q34
#34
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Easy
What is
p
2
+
q
2
p
2
q
2
\dfrac{p^2+q^2}{p^2 q^2}
p
2
q
2
p
2
+
q
2
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
1
2
\dfrac{1}{2}
2
1
B
1
C
3
2
\dfrac{3}{2}
2
3
D
2
Tap an option to check your answer.
Show solution
[Q28 · Sep · 2025]
Report
Q35
#35
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Hard
If
tan
α
=
1
7
,
sin
β
=
1
10
;
0
<
α
,
β
<
π
2
\tan\alpha=\frac{1}{7},\ \sin\beta=\frac{1}{\sqrt{10}};\ 0<\alpha,\beta<\frac{\pi}{2}
tan
α
=
7
1
,
sin
β
=
10
1
;
0
<
α
,
β
<
2
π
, then what is the value of
cos
(
α
+
2
β
)
\cos(\alpha+2\beta)
cos
(
α
+
2
β
)
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
−
1
2
-\frac{1}{\sqrt{2}}
−
2
1
B
−
1
2
-\frac{1}{2}
−
2
1
C
1
2
\frac{1}{2}
2
1
D
1
2
\frac{1}{\sqrt{2}}
2
1
Tap an option to check your answer.
Show solution
[Q30 · Sep · 2023]
Report
Q36
#36
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
What is
3
cos
10
°
−
sin
10
°
sin
25
°
cos
25
°
\dfrac{\sqrt{3}\cos10°-\sin10°}{\sin25°\cos25°}
sin
25°
cos
25°
3
cos
10°
−
sin
10°
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
1
1
1
B
3
3
3
C
2
2
2
D
4
4
4
Tap an option to check your answer.
Show solution
[Q36 · Apr · 2024]
Report
Q37
#37
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
f
(
θ
)
=
1
1
+
tan
θ
f(\theta)=\dfrac{1}{1+\tan\theta}
f
(
θ
)
=
1
+
tan
θ
1
and
α
+
β
=
5
π
4
\alpha+\beta=\dfrac{5\pi}{4}
α
+
β
=
4
5
π
, then what is the value of
f
(
α
)
⋅
f
(
β
)
f(\alpha)\cdot f(\beta)
f
(
α
)
⋅
f
(
β
)
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
−
1
2
-\dfrac{1}{2}
−
2
1
B
1
2
\dfrac{1}{2}
2
1
C
1
1
1
D
2
2
2
Tap an option to check your answer.
Show solution
[Q47 · Apr · 2024]
Report
Q38
#38
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
tan
α
\tan\alpha
tan
α
and
tan
β
\tan\beta
tan
β
are the roots of the equation
x
2
−
6
x
+
8
=
0
x^2-6x+8=0
x
2
−
6
x
+
8
=
0
, then what is the value of
cos
(
2
α
+
2
β
)
\cos(2\alpha+2\beta)
cos
(
2
α
+
2
β
)
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
13
75
\dfrac{13}{75}
75
13
B
13
85
\dfrac{13}{85}
85
13
C
17
85
\dfrac{17}{85}
85
17
D
19
85
\dfrac{19}{85}
85
19
Tap an option to check your answer.
Show solution
[Q48 · Apr · 2024]
Report
Q39
#39
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
What is the value of
tan
65
°
+
2
tan
45
°
−
2
tan
40
°
−
tan
25
°
\tan65°+2\tan45°-2\tan40°-\tan25°
tan
65°
+
2
tan
45°
−
2
tan
40°
−
tan
25°
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
0
0
0
B
1
1
1
C
2
2
2
D
4
4
4
Tap an option to check your answer.
Show solution
[Q49 · Apr · 2024]
Report
Q40
#40
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Easy
What is
cos
17
°
−
sin
17
°
cos
17
°
+
sin
17
°
\dfrac{\cos17°-\sin17°}{\cos17°+\sin17°}
cos
17°
+
sin
17°
cos
17°
−
sin
17°
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
tan
34
°
\tan34°
tan
34°
B
cot
34
°
\cot34°
cot
34°
C
tan
62
°
\tan62°
tan
62°
D
cot
62
°
\cot62°
cot
62°
Tap an option to check your answer.
Show solution
[Q30 · Sep · 2024]
Report
Q41
#41
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Hard
If
x
cos
θ
=
y
cos
(
2
π
3
−
θ
)
=
z
cos
(
2
π
3
+
θ
)
x\cos\theta=y\cos\!\left(\dfrac{2\pi}{3}-\theta\right)=z\cos\!\left(\dfrac{2\pi}{3}+\theta\right)
x
cos
θ
=
y
cos
(
3
2
π
−
θ
)
=
z
cos
(
3
2
π
+
θ
)
, then what is
x
+
y
+
z
x+y+z
x
+
y
+
z
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
−
1
-1
−
1
B
0
0
0
C
1
1
1
D
3
3
3
Tap an option to check your answer.
Show solution
[Q32 · Sep · 2024]
Report
Q42
#42
NDA → Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Hard
If
p
tan
(
θ
−
30
°
)
=
q
tan
(
θ
+
120
°
)
p\tan(\theta-30°)=q\tan(\theta+120°)
p
tan
(
θ
−
30°
)
=
q
tan
(
θ
+
120°
)
, then what is
p
+
q
p
−
q
\dfrac{p+q}{p-q}
p
−
q
p
+
q
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
sin
2
θ
\sin2\theta
sin
2
θ
B
cos
2
θ
\cos2\theta
cos
2
θ
C
2
sin
2
θ
2\sin2\theta
2
sin
2
θ
D
2
cos
2
θ
2\cos2\theta
2
cos
2
θ
Tap an option to check your answer.
Show solution
[Q33 · Sep · 2024]
Report
Prev
Page 2 of 2
Next
1
2
Question Bank
Bank
Guides
Notes
NDA
Sign in