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Question
Prove the following:
`(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`
Solution
L.H.S. = `(sin 5x + sin 3x)/(cos 5x + cos 3x)`
= `(2sin ((5x + 3x)/2) cosx ((5x - 3x)/2))/(2cos ((5x + 3x)/2) cos ((5x - 3x)/2)`
= `(2sin 4x cosx)/(2cos 4x cosx)`
= `(sin 4x)/(cos4x)`
= tan 4x = R.H.S.
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