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Question

Evaluate sinθ1cotθ+cosθ1tanθ=

A
0
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B
1
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C
cosθsinθ
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D
cosθ+sinθ
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Solution

The correct option is D cosθ+sinθ
we have, sinθ1cotθ+cosθ1tanθ

sinθ11tanθ+cosθ1tanθ

sinθtanθtanθ1+cosθ1tanθ

sinθtanθcosθtanθ1

sin2θcosθcosθtanθ1

sin2θcos2θcosθ(tanθ1)

(sinθ+cosθ)(sinθcosθ)cosθ(sinθcosθ1)

(sinθ+cosθ)(sinθcosθ)(sinθcosθ)

sinθ+cosθ

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