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Question
Prove the following:
sin26x − sin24x = sin2x sin10x
Solution
L.H.S. = sin26x − sin24x
= (sin6x + sin4x) (sin6x – sin4x)
= `2sin((6x + 4x)/2)*cos((6x - 4x)/2) xx 2cos((6x + 4x)/2)*sin((6x - 4x)/2)`
= 2sin5x · cosx × 2cos5x · sinx
= 2sin x cosx × 2sin5x · cos5x
= sin2x · sin10x
= R.H.S.
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