Question

The value of (1 + cot²θ)(1 – cos²θ) 

1. 1
2. 2
3. -1
4. -2

Answer 1

Correct Answer - Option 1 : 1

Given:

(1 + cot²θ)(1 – cos²θ)

Formula used:

sin²θ + cos²θ = 1  

cosec²θ – cot²θ = 1

cosecθ = 1/sinθ

Calculation:

(1 + cot²θ)(1 – cos²θ)

⇒ cosec²θ × sin²θ

⇒ 1/sin²θ × sin²θ = 1

∴ The value of (1 + cot²θ)(1 – cos²θ) is 1.