241)

If a = 45° and b = 15°, what is the value of \({\cos (a - b ) - \cos (a + b)} \over {\cos(a - b) + \cos(a + b)}\) ?

SSC CGL 2022

A)

3 - √2

B)

3 - √6

C)

2 - 2√2

D)

2 - √3

242)

What is the value of cosec 15° sec 15°?

SSC CGL 2022

A)

2

B)

4

C)

0.5

D)

1

243)

\(\rm {\cos A \over {1 - \tan A}} + {\sin A \over {1 - \cot A}}\) = ________.

SSC CGL 2022

A)

sin A - cos A

B)

tan A + cot A

C)

tan A - cot A

D)

sin A + cos A

244)

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)

\({\sqrt{3}}\)

245)

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

246)

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

247)

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)

248)

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

249)

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°

250)

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

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