Solve (cot A - 1) / (2 - sec2 A) = (cot A) / (1 + tan A)

Sol:

Given: \(\frac{cot A – 1}{2 – sec^{2}A} = \frac{cot A}{ 1 + tan A}\)

L.H.S = \(\frac{cot A – 1}{2 – sec^{2}A} \) \(\Rightarrow \frac{\frac{1}{tan A} – 1}{2 (1 + tan^{2} A)}\\\Rightarrow \frac{1 – tan A}{tan A (1 – tan) (1 + tan)}\\\Rightarrow \frac{1}{tan A} * \frac{1}{1 + tan A}\\\Rightarrow \frac{cot A}{1 + tan A} RHS\)

Hence it is proved.

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