Question

Prove that:

\[\frac{\sin^4 A + \cos^4 A}{\sin^2 A \cdot \cos^2 A} = \tan^2 A + \cot^2 A\]

Answer 1

Solving L.H.S. of the equation:

\[\Rightarrow \frac{\sin^4 A + \cos^4 A}{\sin^2 A.\cos^2 A}\]

\[\Rightarrow \frac{\sin^4 A}{\sin^2 A.\cos^2 A} + \frac{\cos^4 A}{\sin^2 A.\cos^2 A}\]

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

\[\Rightarrow \tan^2 A + \cot^2 A.\]

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