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Question

How do you use the trigonometric identity cos2x=cos2x-sin2x to verify that cos2x=2cos2x-1.


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Solution

Verify the given identity:

Given identity: cos2x=cos2x-sin2x.

It is known that, cos2x+sin2x=1

sin2x=1-cos2x.

Substitute sin2x with 1-cos2x in given identity

cos2x=cos2x-1-cos2xcos2x=cos2x-1+cos2xcos2x=2cos2x-1

Therefore, the given identity, cos2x=2cos2x-1 is verified.


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