The value of 32/(sec²θ) - 20/(1 + tan²θ) + 12sin²θ is :

SSC Selection Post 2023 PYQ — Question 59

The value of $\frac{32}{sec^2θ} - \frac{20}{1 + tan^2θ} + 12sin^2θ$ is :

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 12.

$\frac{32}{sec^2θ} - \frac{20}{1 + tan^2θ} + 12sin^2θ$

= 32 cos²θ - 20 cos²θ + 12 sin²θ

= 12 cos²θ + 12 sin²θ

= 12(sin²θ + cos²θ)

= 12