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Question

State the whether given equation is true or false
Prove that:cos(π4+x)+cos(π4x)=2cosx

A
True
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B
False
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Solution

The correct option is A True
Prove that
cos(π4+x)+cos(π4x)=2cosx

Apply cos(A+B)=cosAcosBsinAsinB and

cos(AB)=cosAcosB+sinAsinB in LHS

LHS.
=cosπ4coscsinπ4sinx+cosπ4cosx+sinπ4sinx

=2cosπ4cosx

=2×12cosx

=2cosx


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