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Show that (1 + tan2 θ) (1 − sinθ) (1+ sinθ) = 1

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(1 + tan2 θ) (1− sin θ) (1 + sin θ) 

= sec2 (1 – sin2 θ) 

= sec2 θ . cos2 θ 

= \(\frac{1}{cos^2\,\theta}.\)cos2 θ = 1.

[(∵ sec2 θ - tan2 θ = 1) {(a+b)(a-b) = a2 + b2} (sin2 θ + cos2 θ = 1)]

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