Question

1+sec^2xsin^2x=sec^2x

Answer 1

1+sec^2(x)sin^2(x)=sec^2(x)
Then you final answer is 1=1

Answer 2

1 + sec^2(x)sin^2(x) = sec^2(x)
This becomes
1+tan^2(x) = sec^2(x) which is an identity
You could
1 + sin^2(x)/cos^2(x) = sec^2(x)
then
cos^2(x) + sin^2(x) = cos^2(x)sec^2(x)
1 = 1