sin x sin 3x20.= 2sinxin x- COS x

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Solution

We have to prove that sinx−sin3x sin 2 x− cos 2 x =2sinx

The Left Hand Side of the equation.

L.H.S.= sinx−sin3x sin 2 x− cos 2 x

Use the formula.

sinA−sinB=2cos{ A+B 2 }sin{ A−B 2 } cos 2 A− sin 2 A=cos2A

Simplify the Left Hand Side of the equation.

L.H.S.= 2cos{ x+3x 2 }sin{ x−3x 2 } −cos2x = 2cos2xsin( −x ) −cos2x = 2cos2x{ −sinx } { −cos2x } =2sinx

Left hand side is equal to right hand side.

Hence, proved.

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