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

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

1+sec^2 (x) sin^2 (x) = sec^2 (x)

Then you final answer is 1=1