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Question

Prove that

(i) cos(π4+x)+ cos(π4x) = 2 cos x

(ii) cos(3π4+x) cos(3π4x) = 2 sin x

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Solution

(i)LHS= cos(π4 + x ) + cos (π4x)

=2 cos π4 cos x [cos (A+B)+cos(AB)=2cosAcosB]

=(2×12cos x)=2 cosx=RHS.

(ii) LHS=cos(3π4+x)cos(3π4x)

=2sin3π4 sinx

[ cos (A+B) cos (AB)=2 sin A sin B ]

=2 sin(ππ4)sin x

=2 sin π4 sin x [ sin (ππ4)=sinπ4]


= (2×12)sinx=2 sin x=RHS.


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