Question Bank
Bank
Guides
Notes
NDA
Sign in
Filtered questions
41 questions match
Filters
1
Download
· 41
Filtering by:
Principle: Double / half-angle formulas
Clear all
Copy link
Q1
#1
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
If
sin
A
=
3
5
\sin A = \dfrac{3}{5}
sin
A
=
5
3
, where
450
°
<
A
<
540
°
450° < A < 540°
450°
<
A
<
540°
, then
cos
A
2
\cos\dfrac{A}{2}
cos
2
A
is equal to
Add
Lever: Double / half-angle formulas
A
1
10
\dfrac{1}{\sqrt{10}}
10
1
B
−
3
10
-\sqrt{\dfrac{3}{10}}
−
10
3
C
3
10
\dfrac{\sqrt{3}}{\sqrt{10}}
10
3
D
None of the above
Tap an option to check your answer.
Show solution
[Q39 · Apr · 2017]
Report
Q2
#2
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Moderate
If
tan
(
α
+
β
)
=
2
\tan(\alpha+\beta)=2
tan
(
α
+
β
)
=
2
and
tan
(
α
−
β
)
=
1
\tan(\alpha-\beta)=1
tan
(
α
−
β
)
=
1
, then
tan
(
2
α
)
\tan(2\alpha)
tan
(
2
α
)
is equal to
Add
Lever: Double / half-angle formulas
A
−
3
-3
−
3
B
−
2
-2
−
2
C
−
1
3
-\dfrac{1}{3}
−
3
1
D
1
1
1
Tap an option to check your answer.
Show solution
[Q48 · Apr · 2017]
Report
Q3
#3
NDA → Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Moderate
Consider the following for triangle
A
B
C
ABC
A
B
C
: 1.
sin
(
B
+
C
2
)
=
cos
(
A
2
)
\sin\!\left(\dfrac{B+C}{2}\right) = \cos\!\left(\dfrac{A}{2}\right)
sin
(
2
B
+
C
)
=
cos
(
2
A
)
2.
tan
(
B
+
C
2
)
=
cot
(
A
2
)
\tan\!\left(\dfrac{B+C}{2}\right) = \cot\!\left(\dfrac{A}{2}\right)
tan
(
2
B
+
C
)
=
cot
(
2
A
)
3.
sin
(
B
+
C
)
=
cos
A
\sin(B+C) = \cos A
sin
(
B
+
C
)
=
cos
A
4.
tan
(
B
+
C
)
=
−
cot
A
\tan(B+C) = -\cot A
tan
(
B
+
C
)
=
−
cot
A
Which of the above are correct?
Add
Lever: Double / half-angle formulas
A
1 and 3
B
1 and 2
C
1 and 4
D
2 and 3
Tap an option to check your answer.
Show solution
[Q49 · Apr · 2017]
Report
Q4
#4
NDA → Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Moderate
In a triangle
A
B
C
ABC
A
B
C
,
a
−
2
b
+
c
=
0
a - 2b + c = 0
a
−
2
b
+
c
=
0
. The value of
cot
(
A
2
)
cot
(
C
2
)
\cot\!\left(\dfrac{A}{2}\right)\cot\!\left(\dfrac{C}{2}\right)
cot
(
2
A
)
cot
(
2
C
)
is
Add
Lever: Double / half-angle formulas
A
9
2
\dfrac{9}{2}
2
9
B
3
C
3
2
\dfrac{3}{2}
2
3
D
1
Tap an option to check your answer.
Show solution
[Q37 · Sep · 2017]
Report
Q5
#5
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
Suppose
cos
A
\cos A
cos
A
is given. If only one value of
cos
(
A
/
2
)
\cos(A/2)
cos
(
A
/2
)
is possible, then A must be
Add
Lever: Double / half-angle formulas
A
An odd multiple of 90 degrees
B
A multiple of 90 degrees
C
An odd multiple of 180 degrees
D
A multiple of 180 degrees
Tap an option to check your answer.
Show solution
[Q48 · Apr · 2018]
Report
Q6
#6
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Easy
What is
2
tan
θ
1
+
tan
2
θ
\frac{2\tan\theta}{1+\tan^2\theta}
1
+
t
a
n
2
θ
2
t
a
n
θ
equal to?
Add
Lever: Double / half-angle formulas
A
cos
2
θ
\cos 2\theta
cos
2
θ
B
tan
2
θ
\tan 2\theta
tan
2
θ
C
sin
2
θ
\sin 2\theta
sin
2
θ
D
csc
2
θ
\csc 2\theta
csc
2
θ
Tap an option to check your answer.
Show solution
[Q36 · Sep · 2018]
Report
Q7
#7
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Moderate
If
sin
α
+
cos
α
=
p
\sin\alpha + \cos\alpha = p
sin
α
+
cos
α
=
p
, then what is
cos
2
(
2
α
)
\cos^2(2\alpha)
cos
2
(
2
α
)
equal to?
Add
Lever: Double / half-angle formulas
A
p
2
p^2
p
2
B
p
2
−
1
p^2-1
p
2
−
1
C
p
2
(
2
−
p
2
)
p^2(2-p^2)
p
2
(
2
−
p
2
)
D
p
2
+
1
p^2+1
p
2
+
1
Tap an option to check your answer.
Show solution
[Q38 · Apr · 2019]
Report
Q8
#8
NDA → Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Moderate
If
cos
A
=
3
4
\cos A = \dfrac{3}{4}
cos
A
=
4
3
, then what is the value of
sin
A
2
sin
3
A
2
\sin\dfrac{A}{2}\sin\dfrac{3A}{2}
sin
2
A
sin
2
3
A
?
Add
Lever: Double / half-angle formulas
A
5
8
\dfrac{5}{8}
8
5
B
5
16
\dfrac{5}{16}
16
5
C
5
24
\dfrac{5}{24}
24
5
D
7
32
\dfrac{7}{32}
32
7
Tap an option to check your answer.
Show solution
[Q42 · Apr · 2019]
Report
Q9
#9
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Easy
What is
cot
(
A
2
)
−
tan
(
A
2
)
\cot\left(\dfrac{A}{2}\right) - \tan\left(\dfrac{A}{2}\right)
cot
(
2
A
)
−
tan
(
2
A
)
equal to ?
Add
Lever: Double / half-angle formulas
A
tan
A
\tan A
tan
A
B
cot
A
\cot A
cot
A
C
2
tan
A
2\tan A
2
tan
A
D
2
cot
A
2\cot A
2
cot
A
Tap an option to check your answer.
Show solution
[Q68 · Sep · 2019]
Report
Q10
#10
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Easy
What is
cot
A
+
cosec
A
\cot A + \cosec A
cot
A
+
cosec
A
equal to ?
Add
Lever: Double / half-angle formulas
A
tan
(
A
2
)
\tan\left(\dfrac{A}{2}\right)
tan
(
2
A
)
B
cot
(
A
2
)
\cot\left(\dfrac{A}{2}\right)
cot
(
2
A
)
C
2
tan
(
A
2
)
2\tan\left(\dfrac{A}{2}\right)
2
tan
(
2
A
)
D
2
cot
(
A
2
)
2\cot\left(\dfrac{A}{2}\right)
2
cot
(
2
A
)
Tap an option to check your answer.
Show solution
[Q69 · Sep · 2019]
Report
Q11
#11
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Moderate
What is
sin
3
x
+
cos
3
x
+
4
sin
3
x
−
3
sin
x
+
3
cos
x
−
4
cos
3
x
\sin 3x + \cos 3x + 4\sin^3 x - 3\sin x + 3\cos x - 4\cos^3 x
sin
3
x
+
cos
3
x
+
4
sin
3
x
−
3
sin
x
+
3
cos
x
−
4
cos
3
x
equal to?
Add
Lever: Double / half-angle formulas
A
0
B
1
C
2
sin
2
x
2\sin 2x
2
sin
2
x
D
4
cos
4
x
4\cos 4x
4
cos
4
x
Tap an option to check your answer.
Show solution
[Q25 · Apr · 2020]
Report
Q12
#12
NDA → Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Hard
Consider the following statements: 1. If in a triangle ABC,
A
=
2
B
A=2B
A
=
2
B
and
b
=
c
b=c
b
=
c
, then it must be an obtuse-angled triangle. 2. There exists no triangle ABC with
A
=
40
°
A=40°
A
=
40°
,
B
=
65
°
B=65°
B
=
65°
and
a
c
=
sin
40
°
csc
15
°
\frac{a}{c}=\sin 40°\csc 15°
c
a
=
sin
40°
csc
15°
. Which of the above statements is/are correct?
Add
Lever: Double / half-angle formulas
A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
Tap an option to check your answer.
Show solution
[Q30 · Apr · 2020]
Report
Set · 3 questions
Directions for the following three (03) items: Read the following information and answer the three items that follow: Let
t
n
=
sin
n
θ
+
cos
n
θ
t_n = \sin^n\theta + \cos^n\theta
t
n
=
sin
n
θ
+
cos
n
θ
.
Q13
#13
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
What is
t
3
−
t
5
t
5
−
t
7
\frac{t_3-t_5}{t_5-t_7}
t
5
−
t
7
t
3
−
t
5
equal to?
Add
Lever: Double / half-angle formulas
A
t
1
t
3
\frac{t_1}{t_3}
t
3
t
1
B
t
3
t
5
\frac{t_3}{t_5}
t
5
t
3
C
t
5
t
7
\frac{t_5}{t_7}
t
7
t
5
D
t
1
t
7
\frac{t_1}{t_7}
t
7
t
1
Tap an option to check your answer.
Show solution
[Q34 · Apr · 2020]
Report
Q14
#14
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Moderate
What is
t
1
2
−
t
2
t_1^2 - t_2
t
1
2
−
t
2
equal to?
Add
Lever: Double / half-angle formulas
A
cos
2
θ
\cos 2\theta
cos
2
θ
B
sin
2
θ
\sin 2\theta
sin
2
θ
C
2
cos
θ
2\cos\theta
2
cos
θ
D
2
sin
θ
2\sin\theta
2
sin
θ
Tap an option to check your answer.
Show solution
[Q35 · Apr · 2020]
Report
Q15
#15
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Easy
What is the value of
t
10
t_{10}
t
10
where
θ
=
45
°
\theta=45°
θ
=
45°
?
Add
Lever: Double / half-angle formulas
A
1
B
1
4
\frac{1}{4}
4
1
C
1
16
\frac{1}{16}
16
1
D
1
32
\frac{1}{32}
32
1
Tap an option to check your answer.
Show solution
[Q36 · Apr · 2020]
Report
Q16
#16
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Easy
A chord subtends an angle 120° at the centre of a unit circle. What is the length of the chord?
Add
Lever: Double / half-angle formulas
A
2
−
1
\sqrt{2}-1
2
−
1
units
B
3
−
1
\sqrt{3}-1
3
−
1
units
C
2
\sqrt{2}
2
units
D
3
\sqrt{3}
3
units
Tap an option to check your answer.
Show solution
[Q23 · Apr · 2021]
Report
Q17
#17
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Easy
If
tan
A
=
1
7
\tan A = \frac{1}{7}
tan
A
=
7
1
, then what is
cos
2
A
\cos 2A
cos
2
A
equal to?
Add
Lever: Double / half-angle formulas
A
24
25
\frac{24}{25}
25
24
B
18
25
\frac{18}{25}
25
18
C
12
25
\frac{12}{25}
25
12
D
6
25
\frac{6}{25}
25
6
Tap an option to check your answer.
Show solution
[Q32 · Apr · 2021]
Report
Q18
#18
NDA → Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Hard
Let
A
B
C
ABC
A
B
C
be a triangle. If
cos
2
A
+
cos
2
B
+
cos
2
C
=
−
1
\cos 2A+\cos 2B+\cos 2C=-1
cos
2
A
+
cos
2
B
+
cos
2
C
=
−
1
, then which one of the following is correct?
Add
Lever: Double / half-angle formulas
A
sin
A
sin
B
sin
C
=
0
\sin A\sin B\sin C=0
sin
A
sin
B
sin
C
=
0
B
sin
A
sin
B
cos
C
=
0
\sin A\sin B\cos C=0
sin
A
sin
B
cos
C
=
0
C
cos
A
sin
B
sin
C
=
0
\cos A\sin B\sin C=0
cos
A
sin
B
sin
C
=
0
D
cos
A
cos
B
cos
C
=
0
\cos A\cos B\cos C=0
cos
A
cos
B
cos
C
=
0
Tap an option to check your answer.
Show solution
[Q41 · Sep · 2021]
Report
Q19
#19
NDA → Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Hard
In a triangle
A
B
C
ABC
A
B
C
,
sin
A
−
cos
B
−
cos
C
=
0
\sin A - \cos B - \cos C = 0
sin
A
−
cos
B
−
cos
C
=
0
. What is angle
B
B
B
equal to?
Add
Lever: Double / half-angle formulas
A
π
6
\frac{\pi}{6}
6
π
B
π
4
\frac{\pi}{4}
4
π
C
π
3
\frac{\pi}{3}
3
π
D
π
2
\frac{\pi}{2}
2
π
Tap an option to check your answer.
Show solution
[Q27 · Apr · 2022]
Report
Q20
#20
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Moderate
If
α
+
β
=
π
4
\alpha+\beta=\frac{\pi}{4}
α
+
β
=
4
π
and
2
tan
α
=
1
2\tan\alpha=1
2
tan
α
=
1
, then what is
tan
2
β
\tan2\beta
tan
2
β
equal to?
Add
Lever: Double / half-angle formulas
A
1
3
\frac{1}{3}
3
1
B
2
3
\frac{2}{3}
3
2
C
3
4
\frac{3}{4}
4
3
D
3
5
\frac{3}{5}
5
3
Tap an option to check your answer.
Show solution
[Q28 · Apr · 2022]
Report
Q21
#21
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
What is the value of
cos
4
7
π
8
+
cos
4
5
π
8
\cos^4\frac{7\pi}{8}+\cos^4\frac{5\pi}{8}
cos
4
8
7
π
+
cos
4
8
5
π
?
Add
Lever: Double / half-angle formulas
A
3
2
\frac{3}{2}
2
3
B
3
4
\frac{3}{4}
4
3
C
3
8
\frac{3}{8}
8
3
D
3
16
\frac{3}{16}
16
3
Tap an option to check your answer.
Show solution
[Q32 · Apr · 2022]
Report
Q22
#22
NDA → Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Hard
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be the lengths of sides
B
C
,
C
A
,
A
B
BC, CA, AB
B
C
,
C
A
,
A
B
respectively of a triangle
A
B
C
ABC
A
B
C
. If
p
p
p
is the perimeter and
q
q
q
is the area of the triangle, then what is
p
(
p
−
2
a
)
tan
(
A
2
)
p(p-2a)\tan\left(\frac{A}{2}\right)
p
(
p
−
2
a
)
tan
(
2
A
)
equal to?
Add
Lever: Double / half-angle formulas
A
q
B
2q
C
3q
D
4q
Tap an option to check your answer.
Show solution
[Q86 · Apr · 2022]
Report
Q23
#23
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Moderate
What is the value of
tan
(
3
π
8
)
\tan\!\left(\frac{3\pi}{8}\right)
tan
(
8
3
π
)
?
Add
Lever: Double / half-angle formulas
A
2
−
1
\sqrt{2}-1
2
−
1
B
2
+
1
\sqrt{2}+1
2
+
1
C
1
−
2
1-\sqrt{2}
1
−
2
D
−
(
2
+
1
)
-(\sqrt{2}+1)
−
(
2
+
1
)
Tap an option to check your answer.
Show solution
[Q48 · Sep · 2022]
Report
Set · 2 questions
Consider the following for the next two (02) items that follow: Let
sin
?
e
t
a
\sin?eta
sin
?
e
t
a
be the GM of
sin
?
l
p
h
a
\sin?lpha
sin
?
l
p
ha
and
cos
?
l
p
h
a
\cos?lpha
cos
?
l
p
ha
;
a
n
γ
an\gamma
anγ
be the AM of
sin
?
l
p
h
a
\sin?lpha
sin
?
l
p
ha
and
cos
?
l
p
h
a
\cos?lpha
cos
?
l
p
ha
.
Q24
#24
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Moderate
What is
cos
2
β
\cos2\beta
cos
2
β
equal to?
Add
Lever: Double / half-angle formulas
A
(
cos
α
−
sin
α
)
2
(\cos\alpha-\sin\alpha)^{2}
(
cos
α
−
sin
α
)
2
B
(
cos
α
+
sin
α
)
2
(\cos\alpha+\sin\alpha)^{2}
(
cos
α
+
sin
α
)
2
C
(
cos
α
−
sin
α
)
3
(\cos\alpha-\sin\alpha)^{3}
(
cos
α
−
sin
α
)
3
D
(
cos
α
−
sin
α
)
2
2
\dfrac{(\cos\alpha-\sin\alpha)^{2}}{2}
2
(
cos
α
−
sin
α
)
2
Tap an option to check your answer.
Show solution
[Q31 · Apr · 2023]
Report
Q25
#25
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
What is the value of
sec
2
γ
\sec2\gamma
sec
2
γ
?
Add
Lever: Double / half-angle formulas
A
3
−
sin
2
α
5
+
2
sin
2
α
\dfrac{3-\sin2\alpha}{5+2\sin2\alpha}
5
+
2
sin
2
α
3
−
sin
2
α
B
5
+
sin
2
α
3
−
sin
2
α
\dfrac{5+\sin2\alpha}{3-\sin2\alpha}
3
−
sin
2
α
5
+
sin
2
α
C
3
−
2
sin
2
α
4
+
sin
2
α
\dfrac{3-2\sin2\alpha}{4+\sin2\alpha}
4
+
sin
2
α
3
−
2
sin
2
α
D
3
−
sin
2
α
4
+
3
sin
2
α
\dfrac{3-\sin2\alpha}{4+3\sin2\alpha}
4
+
3
sin
2
α
3
−
sin
2
α
Tap an option to check your answer.
Show solution
[Q32 · Apr · 2023]
Report
Prev
Page 1 of 2
Next
1
2
Question Bank
Bank
Guides
Notes
NDA
Sign in