Question

Prove cot2A – cos2A = cot2Acos2A

Answer 1

Let us take the LHS of the equation Cot2A - Cos2A

Cot A = Cos A / Sin A

Cot2A = cos2A / sin2A

substituting the value of cot2A in the above expression, we get

Cos2A / Sin2A - Cos2A.

Taking LCM, and expanding the expression, we get

(Cos2A - Sin2A Cos2A) / Sin2A = Cos2A * (1-Sin2A) / Sin2A

= (Cos2A/Sin2A) * (1-Sin2A)

Cos2A/Sin2A = Cot2A and 1-Sin2A = Cos2A

Thus, we get

(Cos2A/Sin2A) * (1 - Sin2A) = Cot2ACos2A = RHS.

Thus, proved.