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Question
Prove the following:
`(sin x + sin 3x)/(cos x + cos 3x) = tan 2x`
Solution
We have, L.H.S. = `(sin x + sin 3x)/(cos x + cos 3x)`
= `(2sin ((x + 3x)/2) cos ((x - 3x)/2))/(2cos ((x + 3x)/2) cos ((x - 3x)/2)`
= `(2sin2xcos(-x))/(2cos2xcos(-x)`
= `(sin2x)/(cos2x)`
= tan2x = R.H.S.
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