prove that $\frac{\sin 4 \theta+\sin 2 \theta}{1+\cos 2 \theta+\cos 4 \theta}=\tan 2 \theta$

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prove that

$\frac{\sin 4 \theta+\sin 2 \theta}{1+\cos 2 \theta+\cos 4 \theta}=\tan 2 \theta$

written 5.6 years ago by

teamques10 ★ 69k

modified 3.0 years ago by

pedsangini276 • 4.8k

engineering mathematics

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1 Answer

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written 5.6 years ago by

teamques10 ★ 69k

Solution:

$\begin{aligned} \mathrm{LHS} &=\frac{\sin 4 \theta+\sin 2 \theta}{1+\cos 4 \theta+\cos 2 \theta} \ &=\frac{2 . \sin 2 \theta \cdot \cos 2 \theta+\sin 2 \theta}{2 \cos ^{2} 2 \theta+\cos 2 \theta} \ &=\frac{\sin 2 \theta(2 \cos 2 \theta+1)}{\cos 2 \theta(2 \cos 2 \theta+1)} \ &=\tan 2 \theta \end{aligned}$

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