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Question
Prove the following:
`(cos9x - cos5x)/(sin17x - sin 3x) = - (sin2x)/(cos 10x)`
Solution
we know that,
cos A - cos B = -2 sin `((A + B)/2) sin((A - B)/2), sin A - sin B = 2 cos ((A + B)/2) sin ((A - B)/2)`
L.H.S. = `(cos9x - cos5x)/(sin17x - sin 3x)`
= `(-2sin ((9x + 5x)/2) sin ((9x - 5x)/2))/(2cos((17x+3x)/2) sin((17x - 3x)/2))`
= `(-2sin7xsin2x)/(2cos10xsin7x)`
= `(-sin2x)/(cos10x)` = R.H.S.
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