Question

prove that sec Square a +cosec square a= sec square a* cosec square a

Answer 1

hope this helps....!

Answer 2

Proved below.

Step-by-step explanation:

Given:

$sec^2a+cosec^2a=sec^2a \times cosec^2a$

LHS = $sec^2a+cosec^2a$

       = $\frac{1}{cos^2a} +\frac{1}{sin^2a}$    $[sec^2a=\frac{1}{cos^2a}, cosec^2a= \frac{1}{sin^2a} ]$

       = $\frac{sin^2a+cos^2a}{sin^2a\times cos^2a}$

       = $\frac{1}{cos^2asin^2a}$          $[sin^2a+cos^2a=1]$

       = $\frac{1}{cos^2a}\times \frac{1}{cosec^2a}$

      = $sec^2a \times cosec^2a$               $[sec^2a=\frac{1}{cos^2a}, cosec^2a= \frac{1}{sin^2a} ]$

       = RHS.

Hence proved.