161)

If 6tan² α - 2 = 0, (0 < α < 90°), then the value of α is:

SSC CHSL 2021

A)

75°

B)

15°

C)

45°

D)

30°

162)

The value of \(\frac{cos^2 89^\circ \ + \ cos^2 1^\circ}{cos 30^\circ \ sin90^\circ \ - \ sin30^\circ cos90^\circ}\) is:

SSC CHSL 2021

A)

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

B)

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

C)

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

D)

2√3

163)

If tan 3θ = sin 45°. cos 45° + cos 60° and 3 θ is an acute angle, then what will be the value of sin 4θ?

SSC CHSL 2021

A)

\(\frac{\sqrt3}{2}\)

B)

1

C)

\(\frac{1}{\sqrt2}\)

D)

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

164)

If tan θ + cot θ = 3, then what will be the value of tan² θ + cot² θ ?

SSC CHSL 2021

A)

7

B)

-1

C)

1

D)

11

165)

The value of cosec (58° + θ) - sec (32° - θ) + sin 15° sin 35° sec 55° sin 30° sec 75° is:

SSC CHSL 2021

A)

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

B)

2

C)

0

D)

1

166)

If 5 tan A = 12, then what is the value of \(\frac{13 \ sin A \ + \ 20 \ tan A}{15 \ tan A \ - \ 13 \ cos A}\), where A is an acute angle?

SSC CHSL 2021

A)

\(\frac{31}{41}\)

B)

\(\frac{41}{50}\)

C)

\(1\frac{29}{31}\)

D)

\(1\frac{19}{41}\)

167)

If sin²x = 3 cos²x and 0° ≤ x ≤ 90°, then what is the value of \(\frac{x}{2} \)?

SSC CHSL 2021

A)

22.5°

B)

45°

C)

15°

D)

30°

168)

If cosec A = 10, then what is the value of 20 sin A + 9√11 sec A?
Given that A is an acute angle.

SSC CHSL 2021

A)

34

B)

23

C)

32

D)

30

169)

If sec θ - cosec θ = 0 and θ is an acute angle, then what is the value of sec² θ + cosec² θ ?

SSC CHSL 2021

A)

1

B)

2

C)

0

D)

4

170)

If a triangle ABC is right-angled at A, then what is the value of \(\rm \sin\frac{B+C}{2}\cos\frac{B+C}{2}\)?

SSC CHSL 2021

A)

\(\frac{\sqrt3}{4}\)

B)

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

C)

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

D)

√2