Question

Simplify (1 + tan²θ)(1 – sinθ)(1 + sinθ)

Answer 1

(1 + tan²θ)(1 – sinθ)(1 + sinθ)

= (1 + tan²θ)(1 – sin²θ)  ...[∵ (a – b)(a + b) = a² – b²]

= sec²θ . cos²θ   ...[∵ 1 + tan²θ = sec²θ and cos²θ + sin²θ = 1]

= `1/(cos^2 theta) * cos^2 theta`  ...`[∵ sec theta = 1/costheta]`

= 1