Question

tan2theta+cot2theta+2=sec2thetaCosec2theta

Answer 1

tan^2 theta + 1 = sec^2 theta (identity)
cot^2 theta + 1 = cosec^2 theta (identity)
so adding both equations we get the ans

Answer 2

hey mate,

hope this helps you

here is the answer

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LHS.
$= > \: \tan^{2} (x) + \cot^{2} (x) + 2$

$= > \tan^{2} (x) + 1 + \cot^{2} (x) + 1$

$= > \sec^{2} (x) + \cosec^{2} (x)$

$= > \frac{1}{ \cos^{2} (x) } + \frac{1}{ \sin {}^{2} (x) }$

$= > \frac{ \sin {}^{2} (x) + \cos {}^{2} (x) }{ \sin {}^{2} (x). \cos {}^{2} (x) }$

$= > \frac{1}{ \sin {}^{2} (x) \cos {}^{2} (x) }$

$= > \sec {}^{2} (x) . \cosec {}^{2} (x)$

= RHS
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HOPE THIS HELPS YOU

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TH@NkS