81)

If 5sin²θ = 3(1 + cosθ), 0° < θ < 90°, then the value of cosecθ + cotθ is:

SSC CHSL 2021

A)

\(\sqrt{\frac{7}{3}}\)

B)

\(\frac{4}{\sqrt{21}}\)

C)

\(\frac{5}{\sqrt{21}}\)

D)

\(\sqrt{\frac{3}{7}}\)

82)

If \(\frac{4sin^2\theta + 5}{4sin^2\theta-1}\) , then the value of  is:

SSC CHSL 2021

A)

12

B)

3

C)

15

D)

9

83)

If \(0^0<\theta<90^0\), then \(\frac{{\left( {1 - \sin\theta } \right)\left( {\sec\theta + \tan\theta } \right)\tan\theta }}{{\left( {\tan\theta + \sec\theta + 1} \right)\left( {\cot\theta - \text{cosec} \ \theta + 1} \right)}} = ?\)

SSC CHSL 2021

A)

(sin θ)/2 

B)

cos θ 

C)

sin θ  

D)

(cos θ)/2 

84)

If  \(tan A=\frac{{1.1}}{{6}}\) then what is the value of (4cos A - 7sin A)? Given that A is an acute angle.

SSC CHSL 2021

A)

\(2\frac{{41}}{{61}}\)

B)

\(2\frac{{14}}{{61}}\)

C)

\(2\frac{{41}}{{71}}\)

D)

\(2\frac{{14}}{{71}}\)

85)

If  \(\rm \frac{3 \sqrt 3 \sec θ + 4 \tan θ}{3 \tan θ + \sqrt 3 \sec θ} = 2\),  0° < θ < 90°, then the value of cos θ will be:

SSC CHSL 2021

A)

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

B)

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

C)

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

D)

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

86)

Solve the following equation.
2 cos² θ + (4 + √3)sin θ - 2(1 + √3) = 0 where θ is an acute angle.

SSC CHSL 2021

A)

30°

B)

45°

C)

15°

D)

60°

87)

What number should be subtracted from
4(sin⁴60° + cos⁴30°) - (tan²45° - cot²30°) + cos²45° - cosec²45°+ sec²60° to get 2 ?

SSC CHSL 2021

A)

5

B)

4

C)

7

D)

3

88)

If θ is an acute angle and sinθ = cosθ, then the value of 2 tan²θ + sin²θ - 1 is equal to:

SSC CHSL 2021

A)

1

B)

-7

C)

3

D)

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

89)

If A lies between 45° and 540°, and sin A = 0.5, what is the value of A/3 in degrees?

SSC CHSL 2021

A)

170°

B)

160°

C)

165°

D)

175°

90)

If \(cosθ = \rm \frac{2}{3}\) , then 2 sec²θ + 2 tanθ - 6 equals:

SSC CHSL 2021

A)

0

B)

2

C)

4

D)

1