Question

The question is to prove the above mentioned identity.

Answer this as soon as possible and don't attempt if you don't know. Thanks!​

Answer 1

TO PROVE THAT :-

$\sf (sin \ A + cosec \ A)^2+(cos \ A + sec \ A )^2= 7+tan^2\ A+cot^2 \ A$

SOLUTION :-

L.H.S = $\sf (sin \ A+ cosec \ A)^2 +(cos \ A+ sec \ A )^2$

         $= \sf sin^2 A + cosec ^2 A + 2 \ sinA \ cosecA+cos^2 A+sec^2 A+2 \ cosA \ secA\\\\= sin^2A+cos^2A+cosec^2A+sec^2A+ \left(2sinA\times \dfrac{1}{sinA}\right)+\left(2cosA\times \dfrac{1}{cosA}\right)\\\\= 1+cosec^2A+sec^2A+2+2 \\\\= 5 + (1+cot^2A)+(1+tan^2A)\\\\= 7+tan^2A+cot^2A\\\\= R.H.S$

         

Hence proved.

IDENTITIES USED :-

$\bullet \sf \ 1+tan^2A = sec^2 A\\\\\bullet \ 1+cot^2A = cosec^2 A \\\\\bullet \ sin^2A+cos^2A= 1 \\\\\bullet \ cosecA =\dfrac{1}{sinA}\\\\\bullet \ secA = \dfrac{1}{cosA}$

         

Answer 2

Answer:

your correct and verified answer ...