(cos^2(x))(cot^2(x))=(cot^2(x))-(cos^2(x))

Left side: (cos^2 ) ( cot^2x)

= cos^2 x 1/tan^2 x

= cos^2 x (cos^2x) /sin^2x

Right side = cot^2 x - cos^2x

= 1/tan^2 x - cos^2 x

= cos^2x /sin^2 -cos^2x

= cos^2x ( 1-sin^2x)

= cos^2 x (cos^2x)/sin^2x

Now left side = right side that proves the given identity.

Please note that in the step before the last, division by sin^x is left out , so please add that sin^2x.

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