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Chapter 7: Q. 63 (page 496)

In Problems 47-68, establish each identity.

sin3胃sin胃-cos3胃cos胃=2

Short Answer

Expert verified

The identitysin3胃sin胃-cos3胃cos胃=2is established.

Step by step solution

01

Step 1 Given identity is,

sin3胃sin胃-cos3胃cos胃=2.

The Formula used in this problem is,role="math" localid="1646473221053" sinA-B=sinAcosB-cosAsinBsin2胃=2sin胃cos胃.

02

Step 2 Use the formula in the required place and prove that the expression in both the sides are equal.

sin3胃sin胃-cos3胃cos胃=sin3胃cos胃-cos3胃sin胃sin胃cos胃=sin3胃-胃sin胃cos胃=sin2胃sin胃cos胃=2sin胃cos胃sin胃cos胃sin3胃sin胃-cos3胃cos胃=2

Hence, proved.

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