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

Question

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

✓

Answer

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

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