Question

Prove that (cosecθ - cotθ)² = (1 - cosθ)/(1 + cosθ)

Answer 1

Answer:

LHS= (cosecθ - cotθ)²

= $(\frac{1}{sin\alpha } - \frac{cos\alpha }{sin\alpha } )^{2} = (\frac{1-cos\alpha }{sin\alpha } )^{2} \\\\= (\frac{(1-cos\alpha )^{2} }{sin^{2} \alpha } = \frac{(1-cos\alpha)^{2} }{1-cos^{2}\alpha } \\= \frac{(1-cos\alpha )^{2} }{(1-cos\alpha)(1+cos\alpha } = \frac{1-cos\alpha }{1+cos\alpha } = RHS.$

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Answer 2

Step-by-step explanation: