Question

tan^2x/tan^2x-1 + cosec^2x/sec^2-cosec^2 = 1/sin^2x-cos^x

Answer 1

We need to prove that:

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

Let us start with the left side:

We know that 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)