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Prove that (sin x+sin 3 x)/(cos x+cos ...

Prove that
`(sin x+sin 3 x)/(cos x+cos 3 x)=tan 2 x`

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because . (L)= (sin 3 x+sin x)/(cos 3 x+cos x)=(2 sin ((3 x+x)/(2))) . (2 cos ((3 x-x)/(2)))/(. . .) (2 sin 2 x cos x)/(2 cos 2 x cos x) =tan 2 x=(R.H.S) ,
therefore L . H . S=R . H . S .
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V PUBLICATION-TRIGNOMETRC FUNCTIONS-QUESTION BANK
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