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Question
Prove the following:
`(cos9x - cos5x)/(sin17x - sin3x) = - (sin2x)/(cos10x)`
Solution
L.H.S. = `(cos9x - cos5x)/(sin17x - sin3x)`
= `(2sin((9x + 5x)/2)sin((5x - 9x)/2))/(2cos((17x + 3x)/2)sin((17x - 3x)/2)`
= `(2sin7x sin (-2x))/(2cos 10x sin7x)`
= `(-sin 2x)/(cos 10x)`
= R.H.S.
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