61)

If sec²A + tan²A = 3, then what is the value of cot A?

SSC CGL 2022

A)

1

B)

0

C)

\(\frac{1}{\sqrt{3}}\)

D)

\({\sqrt{3}}\)

62)

If θ is an acute angle and tan θ + cot θ = 2, then the value of \(tan^{200} θ + cot^{200} θ\) is:

SSC CGL 2022

A)

-1

B)

2

C)

1

D)

0

63)

If cosec θ + cot θ = p, then the value of \({{p^2 \ - \ 1} \over p^2 \ + \ 1}\) is:

SSC CGL 2022

A)

cot θ

B)

sin θ

C)

cos θ

D)

cosec θ

64)

Find the value of cos 2A cos 2B + sin²(A - B) - sin²(A + B)

SSC CGL 2022

A)

cos (2A + 2B)

B)

sin (2A + 2B)

C)

sin (2A − 2B)

D)

cos (2A − 2B)

65)

Find the value of tan 27° tan 34° + tan 34° tan 29° + tan 29° tan 27°.

SSC CGL 2022

A)

\({\sqrt{3}}\)

B)

–1

C)

0

D)

1

66)

If sin² θ − 3 sin θ + 2 = 0, then find the value of θ (0° ≤ θ ≤ 90°).

SSC CGL 2022

A)

60°

B)

0°

C)

45°

D)

90°

67)

\(\frac{{1 + \sin \theta }}{{\cos \theta }}\) is equal to which of the following (where \(\theta \ne \frac{\pi }{2}\))?

SSC CGL 2022

A)

\(\frac{{\tan \theta - 1}}{{\tan \theta + 1}}\)

B)

\(\frac{{\tan \theta + 1}}{{\tan \theta - 1}}\)

C)

\(\frac{{1 + \cos \theta }}{{\sin \theta }}\)

D)

\(\frac{{\cos \theta }}{{1 - \sin \theta }}\)

68)

If tan3θ⋅tan7θ = 1, where 7θ is an acute angle, then find the value of cot15θ.

SSC CGL 2022

A)

\(-\sqrt3\)

B)

-1

C)

1

D)

\(\sqrt3\)

69)

Find the value of s\(ecθ - tanθ, if secθ + tanθ = \sqrt5\) .

SSC CGL 2022

A)

\(5\frac{\sqrt5}{5}\)

B)

\(5\frac{1}{5}\)

C)

5

D)

\(\sqrt5\)

70)

If \(2 sinθ + 2 sin^2θ=2\), then the value of \(2 cos^4θ + 2 cos^2θ\) is:

 

SSC CGL 2022

A)

1

B)

2

C)

4

D)

0