Q11 of 120 Page 95

Simplify (1+tan2 θ)(1-sin θ)(1+sin θ)

(1+tan2 θ)(1 – sin θ)(1+sin θ)

= sec2 θ (1 – sin θ)(1+sin θ) [∵ 1+tan2 θ = sec2 θ]


= sec2 θ (1 – sin2 θ) [∵ by property, (a+b)(a-b) = a2+b2]


= sec2 θ cos2 θ [∵ 1 – sin2 θ = cos2θ]



= 1


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