31)

If 21 tan θ = 20, then(1 + sin θ - cos θ) : (1 - sin θ + cos θ) is equal to:

, Avg: 01:25 , 66%✓ SSC CHSL 2021

A)

11 ∶ 13

B)

12 ∶ 11

C)

14 ∶ 15

D)

13 ∶ 15

32)

Simplify the following expression.
cos² 30° + cos² 40°+ cos² 50° + cos² 60°

, Avg: 00:20 , 50%✓ SSC CHSL 2021

A)

2

B)

1

C)

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

D)

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

33)

If 5k = tanθ and \({5\over k}= sec\theta\), then what is the value of \(10\left(k^2-\frac{1}{k^2}\right) \) ?

SSC CHSL 2021

A)

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

B)

-2

C)

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

D)

2

34)

If sin θ( 2 sin θ + 3) = 2, 0° < θ < 90°, then what is the value of (sec² θ + cot² θ - cos² θ)?

, Avg: 01:49 , 60%✓ SSC CHSL 2021

A)

\(\frac{43}{12}\)

B)

\(\frac{13}{3}\)

C)

\(\frac{31}{12}\)

D)

\(\frac{7}{2}\)

35)

If \(\sin θ=\frac{11}{15} \), then the value of (sec θ - tan θ) is:

, Avg: 01:11 , 40%✓ SSC CHSL 2021

A)

\(\frac{\sqrt{26}}{13}\)

B)

\(\frac{1}{\sqrt{26}}\)

C)

\(\frac{4}{\sqrt{26}}\)

D)

\(\frac{2\sqrt{26}}{13}\)

36)

\(\frac{(1+\cos \theta)(cosec \theta-\cot \theta)\sec \theta}{\sin \theta(1-\sin\theta)(\sec \theta+\tan \theta)}=?\)

, Avg: 02:26 , 33%✓ SSC CHSL 2021

A)

cos² θ

B)

sin² θ

C)

cosec² θ

D)

sec² θ

37)

If 3cos²θ - 4sinθ + 1 , 0° < θ < 90°, then the value of 3cos²θ + 5tan²θ will be:

, Avg: 01:35 , 57%✓ SSC CHSL 2021

A)

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

B)

\(5\frac{2}{3}\)

C)

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

D)

\(6\frac{2}{3}\)

38)

If \(sin\theta={2\sqrt{ab}\over a+b}\), a > b > 0, then the value of \( \frac{cos\theta + 1}{cos \theta - 1}\) will be:

, Avg: 00:45 , 33%✓ SSC CHSL 2021

A)

\(-\frac{b}{a}\)

B)

\(-\frac{a}{b}\)

C)

\(\frac{a}{b}\)

D)

\(\frac{b}{a}\)

39)

The value of \(\frac{3cos^227^\circ-5 + 3cos^263^\circ }{tan^232^\circ + 4 - cosec^2 58^\circ} \)\(+ sin35°cos55° \)\(+ cos35°sin55°\) is:

, Avg: 00:29 , 55%✓ SSC CHSL 2021

A)

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

B)

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

C)

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

D)

\(1\frac{2}{3}\)

40)

Solve the following equation.
2√3 sin² θ + cos θ – √3 = 0 where θ is an acute angle.

, Avg: 01:37 , 66%✓ SSC CHSL 2021

A)

60°

B)

15°

C)

30°

D)

45°