Question

Prove ((sec^2(x))(sec^2(x)+1)/sin^2(x) +csc^4(x)-tan^2(x)*cos^2(x) = (sec^4(x))/sin^2(x) + sec^2(x)*csc^4(x) - sin^2(x)
is an identity.

Answer 1

The parens on the left are unbalanced.
On the right, we have
(sec^4(x))/sin^2(x) + sec^2(x)*csc^4(x) - sin^2(x)
= 1/(cos^4x sin^2x) + 1/(cos^2x sin^4x) - sin^2x
= (sin^2x+cos^2x)/(cos^4x sin^4x) - sin^2x
= 1/(cos^4x sin^4x) - sin^2x

so, fix the left side and then we can talk.

Answer 2

((sec^2(x)(sec^2(x)+1))/(sin^2(x)) + csc^4(x) - tan^2(x)*cos^2(x)
here is the left side

Answer 3

Is the "+ csc^4(x) - tan^2(x)*cos^2(x)" not part of the denominator of the fraction on the left hand side?