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Question

The value of (1+cotθcosecθ)(1+tanθ+secθ) is

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Solution

(1+cotθcosecθ)(1+tanθ+secθ)
=1+tanθ+secθ+cotθ+cotθtanθ+cotθsecθcosecθcosecθtanθcosecθsecθ
=1+tanθ+secθ+cotθ+(1tanθ×tanθ)+(cosθsinθ×1cosθ)cosecθ(1sinθ×sinθcosθ)cosecθsecθ
=1+tanθ+secθ+cotθ+1+1sinθcosecθ1cosθcosecθsecθ
=1+tanθ+secθ+cotθ+1+cosecθcosecθsecθcosecθsecθ
=2+tanθ+cotθsecθcosecθ
=2+sinθcosθ+cosθsinθ1sinθcosθ
=2sinθcosθ+sin2θ+cos2θ1sinθcosθ=2sinθcosθsinθcosθ=2

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