\(cos\left(a+b\right)cos\left(a-b\right)\)
\(=\dfrac{1}{2}\left[cos\left(a+b+a-b\right)+cos\left(a+b-a+b\right)\right]\)
\(=\dfrac{1}{2}\left(cos2a+cos2b\right)\)
\(=\dfrac{1}{2}\left(2cos^2a-1+2cos^2b-1\right)\)
\(=\dfrac{1}{2}\left(2.\left(\dfrac{3}{5}\right)^2-1+2.\left(-\dfrac{4}{5}\right)^2-1\right)=0\)
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