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Prove that (sin x-sin 3 x)/(sin ^(2) x-...

Prove that
`(sin x-sin 3 x)/(sin ^(2) x-cos ^(2) x)=2 sin x`

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( L.H.S ) =(sin x-sin 3 x)/(sin ^(2) x-cos ^(2) x)=(sin 3 x-sin x)/(cos ^(2) x-sin ^(2) x)=(sin 3 x-sin x)/(cos 2 x) =(2 cos .((3 x+x)/(2)) sin ((3 x-x)/(2)))/(cos 2 x)=(2 cos 2 x sin x)/(. cos 2 x) = 2 sin x= ( R.H.S )
( L.H.S )=(R) . (H.S) .
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V PUBLICATION-TRIGNOMETRC FUNCTIONS-QUESTION BANK
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  2. Prove that (sin x+sin 3 x)/(cos x+cos 3 x)=tan 2 x

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  3. Prove that (sin x-sin 3 x)/(sin ^(2) x-cos ^(2) x)=2 sin x

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  4. Prove that (cos 4 x+cos 3 x+cos 2 x)/(sin 4 x+sin 3 x+sin 2 x)=cot 3 x...

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  5. Prove that cot x cot 2 x-cot 2 x cot 3 x-cot 3 x cot x=1

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  7. Prove that cos 4(x)=1-8 sin ^(2) (x) cos ^(2) (x)

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  8. Prove that cos 6 x=32 cos ^(6) x-48 cos ^(4) x+18 cos ^(2) x-1

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  14. Solve 2 cos ^(2) x+3 sin x=0

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