Question
Prove that $\sec^2 (90^\circ - \theta ) + \tan^2 (90^\circ - \theta ) = 1 + 2 \cot^2 \theta .$
✓
Answer
$LHS = \sec^2 (90^\circ - \theta ) + \tan^2 (90^\circ - \theta )$
$= cosec^2\theta + \cot^2\theta $
$= 1 + \cot^2\theta + \cot^2\theta $
$= 1 + 2cot^2\theta $
$= RHS$
Hence proved.
$= cosec^2\theta + \cot^2\theta $
$= 1 + \cot^2\theta + \cot^2\theta $
$= 1 + 2cot^2\theta $
$= RHS$
Hence proved.
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