21)

The expression (cos⁶ θ + sin⁶ θ-1) (tan²θ + cot²θ + 2) +1 is equal to:

SSC CGL 2022

A)

0

B)

-2

C)

1

D)

-1

22)

The value of 2 - \(\sqrt {\frac{{\cot \theta + \cos \theta }}{{\cot \theta - \cos \theta }}}\), when 0° < θ < 90° is equal to:

SSC CGL 2022

A)

2 – sec θ – tan θ

B)

2 – sec θ + tan θ

C)

2 + sec θ + tan θ

D)

2 + sec θ– tan θ

23)

If A = 10^∘ , what is the value of: \(\frac{{12\sin 3A + 5\cos (5A - {5^ \circ })}}{{9\sin \frac{{9A}}{2} - 4\cos (5A + {{10}^ \circ })}}\)

SSC CGL 2022

A)

 \(\frac{{(9 - 2\sqrt 2 )}}{{6\sqrt 2 + 5)}} \)

B)

 \(\frac{{6\sqrt 2 - 5}}{{(9 - 2\sqrt 2 )}} \)

C)

 \(\frac{{6\sqrt 2 + 5}}{{(9 - 2\sqrt 2 )}} \)

D)

 \(\frac{{6\sqrt 2 + 5}}{{(9 + 2\sqrt 2 )}}\)

24)

If 2 sin² θ + 3 cos θ = 3, 0^∘ < θ < 90^∘ , then the value of ( sec² θ + cot² θ) is

SSC CGL 2022

A)

\(4\frac{1}{3} \)

B)

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

C)

\(3\frac{2}{3} \)

D)

\(4\frac{1}{2} \)

25)

If A = 60°, what is the value of:
\( \frac{{{\rm{10 \ sin }}\frac{{\rm{A}}}{{\rm{2}}}{\rm{ \ + \ 8cosA}}}}{{{\rm{7\ sin }}\frac{{{\rm{3A}}}}{{\rm{2}}}{\rm{ \ - \ 12cosA}}}}={\rm{?}}\)

SSC CGL 2022

A)

7

B)

12

C)

10

D)

9

26)

If 3 sin² θ + 4cos θ - 4 = 0, 0° < θ < 90, then the value of (cosec² θ + cot² θ) is

SSC CGL 2022

A)

17/9

B)

4/3

C)

5/4

D)

25/3

27)

If cos B = 5 / 7 , what is the value of cosec B + cot B? Given that 0 < B < π/2?

SSC CGL 2022

A)

\(\frac{7}{{\sqrt 6 }}\)

B)

\(\frac{{\sqrt 6 }}{{12}}\)

C)

\(\frac{5}{{\sqrt 6 }}\)

D)

\(\sqrt 6\)

28)

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)

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

29)

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°

30)

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