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Question

Prove that cos(π4+x)+cos(π4x)=2cosx

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Solution

Prove that cos(π4+x)+cos(π4x)=2cosx

L. H. S. = cos(π4+x)+cos(π4x)

cos(A+B)+cos(AB)=2cosAcosB

=2cos(π4)cosx


=212×cosx

=2cosx=R.H.S

Hence proved.


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