211)

If cos 53° = x / y , then sec 53° + cot 37° is equal to:

SSC CGL 2022

A)

\(\frac{{y + \sqrt {{y^2} - {x^2}} }}{x}\)

B)

\(\frac{{x + \sqrt {{y^2} - {x^2}} }}{x}\)

C)

\(\frac{{x + \sqrt {{y^2} - {x^2}} }}{y}\)

D)

\(\frac{{y + \sqrt {{y^2} - {x^2}} }}{y}\)

212)

If cot² α + tan² α = 2, 0° ≤ α ≤ 90°, then find the value of α

SSC CGL 2022

A)

45°

B)

60°

C)

90°

D)

0°

213)

Simplify the following expression:
\( \frac{{\cos A}}{{1 - \tan A}} + \frac{{\sin A}}{{1 - \cot A}} - \sin A\)

SSC CGL 2022

A)

1 + sin A

B)

1 + cos A

C)

(1 + sin A) cos A

D)

cos A

214)

Simplify the following expression:
cosec⁴ A(1 - cos⁴ A) - 2 cot² A - 1

SSC CGL 2022

A)

sin² A

B)

0

C)

cosec² A

D)

1

215)

If 6tanA (tanA + 1) = 5 - tanA, Given that  \( 0 < A< \frac{\pi}{2}\) what is the value of (sinA + cosA)?

SSC CGL 2022

A)

\(\frac{5}{{\sqrt 3 }}\)

B)

\(5 \sqrt{3}\)

C)

\(3 \sqrt{5}\)

D)

\(\frac{3}{{\sqrt 5 }}\)

216)

If tan B =5/3, then what is the value of \( cosec B +sin B \over cos B - secB\) ?

SSC CGL 2022

A)

\(59\over15\)

B)

\(177\over 125\)

C)

\(- {177\over125}\)

D)

\(-{59\over15}\)

217)

If tan² A - 6 tan A + 9 = 0, 0 < A < 90°, what is the value of \(6 cot A + 8 \sqrt{10} cos A\)?

SSC CGL 2022

A)

14

B)

10 \(\sqrt{10}\)

C)

8 \(\sqrt{10}\)

D)

10

218)

The value of \(\left(\frac{1-\cot θ}{1-\tan θ}\right)^{2} + 1\), if 0° < θ < 90°, is equal to:

SSC CGL 2022

A)

sec²θ

B)

sin²θ

C)

cosec²θ

D)

cos²θ

219)

The value of \(\frac{5 \cos ^{2} 62^{\circ}+5 \cos ^{2} 28^{\circ}-21}{7 \sin ^{2} 35^{\circ}+7 \sin ^{2} 55^{\circ}+1}\) is:

SSC CGL 2022

A)

2

B)

3

C)

-2

D)

-3

220)

If A = 30°, what is the value of: \(\frac{\left[8 \sin \mathrm{A}+11 \operatorname{cosec} \mathrm{A}-\cot ^{2} \mathrm{A}\right]}{10 \cos 2 \mathrm{A}}\) ?

SSC CGL 2022

A)

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

B)

\(4 \frac{2}{5}\)

C)

\(3 \frac{4}{5}\)

D)

\(4 \frac{3}{5}\)