Question

pls solve this question

Answer 1

Here's your Answer

Question
$\sqrt \dfrac{sec - 1} {sec + 1}$ + $\sqrt \dfrac{sec + 1} {sec - 1}$ =2cosec

Answer : Taking LHS

$\dfrac{(sec-1)^2 + (sec+1)^2} {sec^2 - 1}$

$\sqrt\dfrac{sec^2+1-2sec + sec^2+1+2sec^2} {sec^2 - 1}$

$\sqrt\dfrac{2sec^2+2} {tan^2}$

$\sqrt\dfrac{2(sec^2 + 1)} {tan^2}$

$\sqrt\dfrac{2(sec^2 + 1) cos^2} {sin^2}$

$\sqrt\dfrac{2(1/cos^2 + 1)cos^2} {sin^2}$

$\sqrt\dfrac{2(1+1)} {sin^2}$

$\sqrt\dfrac{4} {sin^2}$

$\dfrac{2} {sin}$

$2 × \dfrac{1} {sin}$

2 × cosec = RHS

Hope it helps you :)
Thank you!

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