Prove that: 1- 2x+ 2x 1+ 2x+ 2x = - Vidyadip

Question

Prove that: $\frac{1-\cos2\text{x}+\sin2\text{x}}{1+\cos2\text{x}+\sin2\text{x}}=\tan\text{x}$

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Answer

$\text{LHS}=\frac{1-\cos2\text{x}+\sin2\text{x}}{1+\cos2\text{x}+\sin2\text{x}}$ $=\frac{2\sin^2\text{x}+2\sin\text{x},\cos\text{x}}{2\cos^2+2\sin\text{x},\cos\text{x}}$ $=\frac{2\sin\text{x}(\sin\text{x}+\cos\text{x})}{2\cos\text{x}(\cos\text{x}+\sin\text{x})}$ $=\frac{\sin\text{x}}{\cos\text{x}}$ $=\tan\text{x}=\text{RHS}$

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