Question

Prove that:

\[2 \cos^2 A + \frac{2}{1 + \cot^2 A} = 2\]

Answer 1

Solving L.H.S. of the equation:

\[\Rightarrow 2 \cos^2 A + \frac{2}{1 + \cot^2 A}\]

By formula,

\[1 + \cot^2 A = \operatorname{cosec}^2 A\]

\[\Rightarrow 2 \cos^2 A + \frac{2}{\operatorname{cosec}^2 A}\]

\[\Rightarrow 2 \cos^2 A + 2 \sin^2 A\]

\[\Rightarrow 2(\cos^2 A + \sin^2 A)\]

By formula,

\[\sin^2 A + \cos^2 A = 1\]

\[\Rightarrow 2 \times 1\]

\[\Rightarrow 2.\]

Since, L.H.S. = R.H.S.