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Use the sum-to-product identities to rewrite the following expression as a product.sin(x) – sin(3x)

Use the sum-to-product identities to rewrite the following expression as a product-example-1
User Amit Vikram Singh
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1 Answer

26 votes
26 votes

Given:


\sin x-\sin 3x

Sol:.

Formula of sin3A is:


\sin 3A=3\sin A-4\sin ^3A

Put the value of sin3x in given function:


\begin{gathered} =\sin x-\sin 3x \\ =\sin x-(3\sin x-4\sin ^3x) \\ =\sin x-3\sin x+4\sin ^3x \\ =-2\sin x+4\sin ^3x \\ =2\sin x(2\sin ^2x-1) \end{gathered}

User Muhammed Jaseem
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