Prove cotθ −cscθ cotθ +cscθ =cosθ −1cosθ +1

LHS=cotθ−cosecθcotθ+cosecθ=sinθcosθ−sinθ1sinθcosθ+sinθ1=sinθcosθ−1sinθcosθ+1=cosθ−1cosθ+1=RHShence proved

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Prove $\frac{cot θ + csc θ}{cot θ - csc θ} = \frac{cos θ + 1}{cos θ - 1}$

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Prove

\frac{cot θ + csc θ}{cot θ - csc θ} = \frac{cos θ + 1}{cos θ - 1}

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L H S = \frac{cot θ + cosec θ}{cot θ - cosec θ} = \frac{\frac{cos θ}{sin θ} + \frac{1}{sin θ}}{\frac{cos θ}{sin θ} - \frac{1}{sin θ}} = \frac{\frac{cos θ + 1}{sin θ}}{\frac{cos θ - 1}{sin θ}} = \frac{cos θ + 1}{cos θ - 1} = R H S

hence proved

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Question Text	Prove $\frac{cot θ + csc θ}{cot θ - csc θ} = \frac{cos θ + 1}{cos θ - 1}$
Answer Type	Text solution:1
Upvotes	150