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Prove that:(cos9x-cos5x)/(sin17 x-sin3x)...

Prove that:`(cos9x-cos5x)/(sin17 x-sin3x)=-(sin2x)/(cos10 x)`

Text Solution

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LHS `=(cos9x-cos5x)/(sin17x-sin3x)`
`=(2sin(9x+5x)/(2)sin(5x-9x)/(2))/(2cos(17x+3x)/(2)sin(17-3x)/(2))`
`=(2sin7xsin(-2x))/(2cos10xsin7x) = (sin(-2x))/(cos10x) = (-sin2x)/(cos10x)` = RHS Hence Proved.
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