prove that cotA-cot2A=cosec2A
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LHS= cotA - cot 2A
=cos A/sin A - cos 2A /sin 2A
=(cosA sin2A- sinAcos 2A)/(sinAsin2A)
=(Sin 2A cos A - cos2AsinA)/(sinA sin2A)
Here we used sinXcosY-sinYcosX=sin(X-Y)
= sin(2A-A)/(sinAsin2A)
=sinA/(sinAsin2A)
=1/sin2A
=cosec2A
=RHS
=cos A/sin A - cos 2A /sin 2A
=(cosA sin2A- sinAcos 2A)/(sinAsin2A)
=(Sin 2A cos A - cos2AsinA)/(sinA sin2A)
Here we used sinXcosY-sinYcosX=sin(X-Y)
= sin(2A-A)/(sinAsin2A)
=sinA/(sinAsin2A)
=1/sin2A
=cosec2A
=RHS
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