Question
Prove the following.
$cot^2\theta - tan^2\theta = cosec^2\theta - sec^2\theta $
$cot^2\theta - tan^2\theta = cosec^2\theta - sec^2\theta $
✓
Answer
Taking LHS
$cot^2\theta - tan^2\theta $
$[ Now, cosec^2\theta - 1 = cot^2\theta and sec^2\theta - 1 = tan^2\theta ]$
$= cosec^2\theta - 1 - (sec^2\theta - 1)$
$= cosec^2\theta - sec^2\theta $
= RHS
Proved !
$cot^2\theta - tan^2\theta $
$[ Now, cosec^2\theta - 1 = cot^2\theta and sec^2\theta - 1 = tan^2\theta ]$
$= cosec^2\theta - 1 - (sec^2\theta - 1)$
$= cosec^2\theta - sec^2\theta $
= RHS
Proved !
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