Question

prove that sec²@ cosec²@ can never be less than 2

Answer 1

You need to know that $\sec^2 \theta . \csc^2 \theta = \sec^2 \theta + \csc^2 \theta$.

Proof:$\sec^2 \theta . \csc^2 \theta = \frac{1}{\sin^2 \theta . \cos^2 \theta} = \frac{ \sin^2 + \cos^2 \theta }{ \sin^2 \theta . \\cos^2 \theta } = \sec^2 \theta + \csc^2 \theta$.

Now each of the terms is greater than 1, hence their sum is greater than 2.