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