SSC CHSL 2021 PYQ — Question 54

The correct answer is Option 4 i.e. 30°.

Given:

7 sin² θ +  3 cos² θ = 4

Formula Used:

cos² θ = 1 - sin² θ

Explanation:

According to the given question,

7 sin² θ +  3 cos² θ = 4

⇒ 7 sin² θ +  3 (1 - sin² θ) = 4

⇒ 7 sin² θ +  3 - 3 sin² θ = 4

⇒ 4 sin² θ = 1

⇒ sin² θ = $1\over 4$

⇒ sin θ = $1\over 2$

⇒ sin θ = sin 30° 

⇒ θ = 30° 

Hence the required answer is 30° .