Question

Prove that sin2x/1-cos2x = cot x.

Answer 1

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your answer is in the picture..


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Answer 2

Answer:

$\frac{sin2x}{1-cos2x}=cotx$

Step-by-step explanation:

$LHS=\frac{sin2x}{1-cos2x}\\=\frac{2sinxcosx}{1-(cos^{2}x-sin^{2}x)}\\=\frac{2sinxcosx}{1-(1-sin^{2}x)+sin^{2}x}\\=\frac{2sinxcosx}{1-1+sin^{2}x+sin^{2}x}\\=\frac{2sinxcosx}{2sin^{2}x}\\=\frac{cosx}{sinx}\\=cotx\\=RHS$

Therefore,

$\frac{sin2x}{1-cos2x}=cotx$

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