Question

The value of (1 + tan² θ) (1 – sin θ) (1 + sin θ) = ______.

Answer 1

The value of (1 + tan² θ) (1 – sin θ) (1 + sin θ) = 1.

Explanation:

(1 + tan² θ) (1 – sin θ) (1 + sin θ)

= sec²θ (1 – sin θ) (1 + sin θ)

= sec²θ (1 – sin²θ)   ...[∵ (a – b)(a + b) = a² – b²]

= sec²θ × cos²θ

= `1/(cos^2θ) xx cos^2θ`

= 1