Square of cosine of difference of angle

\[(Cos A+Cos B)^{2}+(Sin A+Sin B)^{2}=4 cos^{2}\frac{A-B}{2} \]

For A=180 B=90

We have

 \[LHS=(Cos 180+Cos90 )^{2}+(Sin 180+Sin 90)^{2}= 2 \]

Similarly

 \[RHS=4cos^{2}\frac{180-90}{2}=2 \]

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