Question

Prove that cosec. ^2+sec.^2=tan^2+cot^2+2

Answer 1

cosec^2x=cot^2x+1
sec^2x=tan^2x+1
adding botj equation
we got the following result
cosec. ^2+sec.^2=tan^2+cot^2+2

Answer 2

Hi...☺

Here is your answer...✌
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$LHS \\ \\= \cosec {}^{2} \alpha + \sec {}^{2} \alpha \\ \\ = 1 + \cot {}^{2} \alpha + 1 + \tan {}^{2} \alpha \\ \\ = \tan {}^{2} \alpha + \cot {}^{2} \alpha + 2 \\ \\ = RHS \\ \\ Hence \: proved$