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Prove that: (sintheta+sin3theta+sin5thet...

Prove that:` (sintheta+sin3theta+sin5theta+… to n terms)/(costheta+cos3theta+cos5theta+…to n terms)= tan ntheta`

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Prove that : (sin theta + sin 3theta + sin 5theta)/(cos theta + cos 3theta + cos 5theta) = tan 3theta

Prove that :(sin theta+sin3 theta+sin5 theta)/(cos theta+cos3 theta+cos5 theta)=tan3 theta

Prove that (sin theta + sin 3theta+ sin 5 theta + sin 7theta)/(cos theta + cos 3theta + cos 5 theta + cos 7theta) = (tan 3theta + tan theta)/(1 - tan 3theta tan theta) .

Prove that : (sin 5theta - 2 sin 3theta + sin theta)/(cos 5theta -cos theta) = tan theta

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(sin theta+sin3 theta+sin5 theta)/(cos theta+cos3 theta+cos5 theta)=tan3 theta

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Prove that :(sin5 theta-2sin3 theta+sin theta)/(cos5 theta-cos theta)=tan theta

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Prove the following identities : (sin theta +sin 3 theta + sin 5 theta + sin 7theta)/(cos theta + cos 3 theta + cos 5 theta + cos 7 theta)=tan 4 theta