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Question

How do you prove cos2x=2cos2x-1?


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Solution

Proof of given relation:

cos2x=2cos2x-1

Here we have LHS=cos2x

Therefore,

cos2x=cosx+x [cosA+B=cosAcosB-sinAsinB]

=cosxcosx-sinxsinx

=cos2x-sin2x

=cos2x-1-cos2x [sin2x+cos2x=1]

=2cos2x-1

=RHS

Hence, cos2x=2cos2x-1 is proved.


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