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
Q26
#26
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
If
2
sec
4
β
=
tan
2
α
+
cot
2
α
2\sec4\beta=\tan2\alpha+\cot2\alpha
2
sec
4
β
=
tan
2
α
+
cot
2
α
, then which one of the following is a possible value of
(
α
+
β
)
(\alpha+\beta)
(
α
+
β
)
?
Add
Lever: AM-GM / mean inequalities (incl. x + 1/x ≥ 2)
A
π
2
\dfrac{\pi}{2}
2
π
B
π
4
\dfrac{\pi}{4}
4
π
C
π
6
\dfrac{\pi}{6}
6
π
D
π
8
\dfrac{\pi}{8}
8
π
Tap an option to check your answer.
Show solution
[Q26 · Apr · 2026]
Report
Q27
#27
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
If
x
=
sec
θ
−
tan
θ
x=\sec\theta-\tan\theta
x
=
sec
θ
−
tan
θ
and
y
=
csc
θ
+
cot
θ
y=\csc\theta+\cot\theta
y
=
csc
θ
+
cot
θ
, then which one of the following is correct?
Add
Lever: Double / half-angle formulas
A
x
+
y
−
x
y
−
1
=
0
x+y-xy-1=0
x
+
y
−
x
y
−
1
=
0
B
x
−
y
+
x
y
+
1
=
0
x-y+xy+1=0
x
−
y
+
x
y
+
1
=
0
C
x
+
y
+
x
y
−
1
=
0
x+y+xy-1=0
x
+
y
+
x
y
−
1
=
0
D
x
−
y
+
x
y
−
1
=
0
x-y+xy-1=0
x
−
y
+
x
y
−
1
=
0
Tap an option to check your answer.
Show solution
[Q28 · Apr · 2026]
Report
Q28
#28
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Moderate
If
cos
θ
=
1
3
\cos\theta=\dfrac{1}{3}
cos
θ
=
3
1
, then what is the value of
sin
(
θ
2
)
sin
(
3
θ
2
)
\sin\!\left(\dfrac{\theta}{2}\right)\sin\!\left(\dfrac{3\theta}{2}\right)
sin
(
2
θ
)
sin
(
2
3
θ
)
?
Add
Lever: Double / half-angle formulas
A
5
9
\dfrac{5}{9}
9
5
B
7
9
\dfrac{7}{9}
9
7
C
10
9
\dfrac{10}{9}
9
10
D
11
9
\dfrac{11}{9}
9
11
Tap an option to check your answer.
Show solution
[Q29 · Apr · 2026]
Report
Q29
#29
NDA → Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Hard
In a triangle ABC,
sin
A
=
cos
B
+
cos
C
\sin A=\cos B+\cos C
sin
A
=
cos
B
+
cos
C
, then what is
tan
(
B
2
)
+
cot
(
B
2
)
\tan\!\left(\dfrac{B}{2}\right)+\cot\!\left(\dfrac{B}{2}\right)
tan
(
2
B
)
+
cot
(
2
B
)
equal to?
Add
Lever: Double / half-angle formulas
A
1
B
2
\sqrt{2}
2
C
3
\sqrt{3}
3
D
2
Tap an option to check your answer.
Show solution
[Q33 · Apr · 2026]
Report
Q30
#30
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Easy
If
x
+
1
x
=
2
cos
θ
x+\dfrac{1}{x}=2\cos\theta
x
+
x
1
=
2
cos
θ
, then what is
x
3
+
1
x
3
x^3+\dfrac{1}{x^3}
x
3
+
x
3
1
equal to?
Add
Lever: Double / half-angle formulas
A
cos
3
θ
\cos^3\theta
cos
3
θ
B
cos
3
θ
\cos3\theta
cos
3
θ
C
2
cos
3
θ
2\cos3\theta
2
cos
3
θ
D
3
cos
3
θ
3\cos3\theta
3
cos
3
θ
Tap an option to check your answer.
Show solution
[Q48 · Sep · 2025]
Report
Set · 2 questions
Let
p
=
1
3
−
tan
3
x
tan
x
p=\dfrac{1}{3}-\dfrac{\tan 3x}{\tan x}
p
=
3
1
−
tan
x
tan
3
x
and
q
=
1
−
3
tan
2
x
,
0
<
x
<
π
,
x
≠
π
2
q=1-3\tan^2 x,\ 0<x<\pi,\ x\neq\dfrac{\pi}{2}
q
=
1
−
3
tan
2
x
,
0
<
x
<
π
,
x
=
2
π
.
Q31
#31
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
What is
p
q
pq
pq
equal to?
Add
Lever: Double / half-angle formulas
A
1
B
2
C
8
3
\frac{8}{3}
3
8
D
−
8
3
-\frac{8}{3}
−
3
8
Tap an option to check your answer.
Show solution
[Q75 · Sep · 2023]
Report
Q32
#32
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Moderate
For how many values of
x
x
x
does
1
p
\frac{1}{p}
p
1
become zero?
Add
Lever: Double / half-angle formulas
A
No value
B
Only one value
C
Only two values
D
Only three values
Tap an option to check your answer.
Show solution
[Q76 · Sep · 2023]
Report
Set · 2 questions
Let
sin
x
+
sin
y
=
3
(
cos
y
−
cos
x
)
\sin x+\sin y=\sqrt{3}(\cos y-\cos x)
sin
x
+
sin
y
=
3
(
cos
y
−
cos
x
)
;
x
+
y
=
π
2
x+y=\frac{\pi}{2}
x
+
y
=
2
π
,
0
<
x
,
y
<
π
2
0<x,y<\frac{\pi}{2}
0
<
x
,
y
<
2
π
.
Q33
#33
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
What is a value of
sin
3
x
+
sin
3
y
\sin3x+\sin3y
sin
3
x
+
sin
3
y
?
Add
Lever: Double / half-angle formulas
A
-1
B
0
C
1
D
3
\sqrt{3}
3
Tap an option to check your answer.
Show solution
[Q77 · Sep · 2023]
Report
Q34
#34
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
What is a value of
cos
3
x
+
cos
3
y
\cos^3x+\cos^3y
cos
3
x
+
cos
3
y
?
Add
Lever: Double / half-angle formulas
A
3
3
8
\frac{3\sqrt{3}}{8}
8
3
3
B
3
6
8
\frac{3\sqrt{6}}{8}
8
3
6
C
3
6
4
\frac{3\sqrt{6}}{4}
4
3
6
D
1
Tap an option to check your answer.
Show solution
[Q78 · Sep · 2023]
Report
Q35
#35
NDA → Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Moderate
Triangle
A
B
C
ABC
A
B
C
such that
∠
C
=
60
°
\angle C=60°
∠
C
=
60°
, then what is
cos
A
+
cos
B
cos
(
A
−
B
2
)
\dfrac{\cos A+\cos B}{\cos\!\left(\dfrac{A-B}{2}\right)}
cos
(
2
A
−
B
)
cos
A
+
cos
B
equal to?
Add
Lever: Double / half-angle formulas
A
2
\sqrt{2}
2
B
2
2
2
C
1
1
1
D
1
2
\dfrac{1}{2}
2
1
Tap an option to check your answer.
Show solution
[Q41 · Apr · 2024]
Report
Q36
#36
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
B
=
16
AB=16
A
B
=
16
cm,
B
C
=
63
BC=63
B
C
=
63
cm and
A
C
=
65
AC=65
A
C
=
65
cm. What is the value of
cos
2
A
+
cos
2
B
+
cos
2
C
\cos2A+\cos2B+\cos2C
cos
2
A
+
cos
2
B
+
cos
2
C
?
Add
Lever: Double / half-angle formulas
A
−
1
-1
−
1
B
0
0
0
C
1
1
1
D
76
65
\dfrac{76}{65}
65
76
Tap an option to check your answer.
Show solution
[Q46 · Apr · 2024]
Report
Q37
#37
NDA → Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Moderate
The roots of the equation
7
x
2
−
6
x
+
1
=
0
7x^2-6x+1=0
7
x
2
−
6
x
+
1
=
0
are
tan
α
\tan\alpha
tan
α
and
tan
β
\tan\beta
tan
β
, where
2
α
2\alpha
2
α
and
2
β
2\beta
2
β
are the angles of a triangle. Which one of the following is correct?
Add
Lever: Double / half-angle formulas
A
The triangle is equilateral
B
The triangle is isosceles but not right-angled
C
The triangle is right-angled
D
The triangle is right-angled isosceles
Tap an option to check your answer.
Show solution
[Q24 · Sep · 2024]
Report
Set · 3 questions
Let
p
=
tan
2
α
−
tan
α
p = \tan 2\alpha - \tan\alpha
p
=
tan
2
α
−
tan
α
and
q
=
cot
α
−
cot
2
α
q = \cot\alpha - \cot 2\alpha
q
=
cot
α
−
cot
2
α
.
Q38
#38
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
What is
p
q
\frac{p}{q}
q
p
equal to?
Add
Lever: Double / half-angle formulas
A
−
tan
α
⋅
tan
2
α
-\tan\alpha\cdot\tan 2\alpha
−
tan
α
⋅
tan
2
α
B
−
cot
α
⋅
cot
2
α
-\cot\alpha\cdot\cot 2\alpha
−
cot
α
⋅
cot
2
α
C
tan
α
⋅
tan
2
α
\tan\alpha\cdot\tan 2\alpha
tan
α
⋅
tan
2
α
D
cot
α
⋅
cot
2
α
\cot\alpha\cdot\cot 2\alpha
cot
α
⋅
cot
2
α
Tap an option to check your answer.
Show solution
[Q41 · Apr · 2025]
Report
Q39
#39
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
What is
(
p
+
q
)
(p + q)
(
p
+
q
)
equal to?
Add
Lever: Double / half-angle formulas
A
sec
4
α
\sec 4\alpha
sec
4
α
B
csc
4
α
\csc 4\alpha
csc
4
α
C
2
sec
4
α
2\sec 4\alpha
2
sec
4
α
D
2
csc
4
α
2\csc 4\alpha
2
csc
4
α
Tap an option to check your answer.
Show solution
[Q42 · Apr · 2025]
Report
Q40
#40
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Hard
What is
tan
2
α
\tan^2\alpha
tan
2
α
equal to?
Add
Lever: Double / half-angle formulas
A
p
q
p
+
q
\frac{pq}{p+q}
p
+
q
pq
B
p
+
2
q
p
\frac{p+2q}{p}
p
p
+
2
q
C
p
p
+
2
q
\frac{p}{p+2q}
p
+
2
q
p
D
p
2
p
+
q
\frac{p}{2p+q}
2
p
+
q
p
Tap an option to check your answer.
Show solution
[Q43 · Apr · 2025]
Report
Set · 1 question
Let
2
sin
α
+
cos
α
=
2
2\sin\alpha + \cos\alpha = 2
2
sin
α
+
cos
α
=
2
, where
0
<
α
<
90
°
0 < \alpha < 90°
0
<
α
<
90°
.
Q41
#41
NDA → Mathematics → Trigonometric Identities → Multiple and Half-Angle Formulas
·
Moderate
What is
2
sin
2
α
+
cos
2
α
2\sin 2\alpha + \cos 2\alpha
2
sin
2
α
+
cos
2
α
equal to?
Add
Lever: Double / half-angle formulas
A
11
10
\frac{11}{10}
10
11
B
11
5
\frac{11}{5}
5
11
C
12
5
\frac{12}{5}
5
12
D
13
5
\frac{13}{5}
5
13
Tap an option to check your answer.
Show solution
[Q45 · Apr · 2025]
Report
Prev
Page 2 of 2
Next
1
2
Question Bank
Bank
Guides
Notes
NDA
Sign in