RHS

=cot²(x)- cos²(x)= cos²(x)/sin²(x) - cos²(x) = (cos²(x) - cos²(x)sin²(x))/sin²(x) = cos²(x)(1 - sin²(x))/sin²(x) = cos²(x) * cos²(x)/sin²(x) = cos²(x)cot²(x) = LHS...................

RHS=LHS....................hence proved

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