Question

Prove that (cosec^2 x/cosec x)-(cosec^2 x/cosec x+1)=2sec^2 x

Answer 1

 secx= 1/cosx   and csec x = 1/sinx

==> sec^2 x+ cosec^2 x= 1/cos^2 x + 1/sin^2 x

= (sen^2 x + cos^2 x)/(sin^2 x)(cos^2 x)

Now we know that sin^2 x + cos^2 x= 1

==> 1/(sin^2 x)(cos^2 x)= (1/sin^2 x)(1/cos^2 x)

= (sec^2 x)*(csec^2 x)