51)

If \(Cos A = {{9} \over 41} \), find cot A.

SSC CGL 2022

A)

\({{40} \over 9}\)

B)

\({{41} \over 40}\)

C)

\({{9} \over 40} \)

D)

\({{9} \over 41}\)

52)

If tan² θ = 1 - a², then the value of sec θ + tan³ θ cosec θ is:

SSC CGL 2022

A)

\((2 - a^2)^{{3} \over 2}\)

B)

\((a^2 - 1)^{{3} \over 2}\)

C)

\((2-a)^{{3} \over 2}\)

D)

\(a^{{3} \over 2}\)

53)

If tan (α + β) = a, tan (α - β) = b, then the value of tan 2α is :

SSC CGL 2022

A)

\(\rm \frac{a-b}{1+ab}\)

B)

\(\rm \frac{a+b}{1+ab}\)

C)

\(\rm \frac{a+b}{1-ab}\)

D)

\(\rm \frac{a-b}{1-ab}\)

54)

If A is an acute angle, the simplified form of
 \(\rm \frac{{\cos (\pi - A).\cot \left( {\frac{\pi }{2} + A} \right)\cos ( - A)}}{{\tan (\pi + A)\tan \left( {\frac{{3\pi }}{2} + A} \right)\sin (2\pi - A)}}\) is :

SSC CGL 2022

A)

Sin² A

B)

Sin A

C)

Cos² A

D)

Cos A

55)

If \(sec \theta + \frac{1}{cos \theta}=2\), find the value of \(sec^{55} \theta + \frac{1}{sec ^{55} \theta}\).

SSC CGL 2022

A)

1

B)

0

C)

2

D)

55

56)

If \({tan40^0}={\alpha}\) , then find\(\frac{tan320^0 - tan 310^0}{1 + tan320^0.tan 310^0}\) .

SSC CGL 2022

A)

\(\frac{1 - \alpha^2}{2\alpha}\)

B)

\(\frac{1 + \alpha^2}{2\alpha}\)

C)

\(\frac{1 - \alpha^2}{\alpha}\)

D)

\(\frac{1 +\alpha^2}{\alpha}\)

57)

If \( tan^2\theta + tan^4\theta = 1 \), then:

SSC CGL 2022

A)

\(sin^2 \theta+sin^4\theta =1\)

B)

\(cos^2 \theta+cos^4\theta =1\)

C)

\(cot^2 \theta+cot^4\theta =1~\)

D)

\(cosec^2 \theta+sec^4\theta =1\)

58)

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

59)

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

SSC CGL 2022

A)

2

B)

4

C)

0.5

D)

1

60)

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

SSC CGL 2022

A)

sin A - cos A

B)

tan A + cot A

C)

tan A - cot A

D)

sin A + cos A