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Prove that: sin2x+2sin4x+sin6x=4cos^2xsi...

Prove that: `sin2x+2sin4x+sin6x=4cos^2xsin4x`

Text Solution

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`LHS=sin2x+2sin4x+sin6x`
`=[sin2x+sin6x]+2sin4x`
`=[2sin((2x+6x)/2)cos((2x-6x)/2)]+2sin4x`
`=2sin4xcos2x+2sin4x`
`=2sin4x(cos2x+1)`
`=2sin4x xx 2 cos^2x`
`=4cos^2x sin4x`
`=RHS`
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