Question

prove sec^4 theta - sec^2theta = tan ^4theta + tan ^2 theta.

Answer 1

sec^4 theta - sec^2 theta
= sec^2 theta ( sec^2 theta - 1 )
Now, 1+tan^2 theta = sec^2 theta
Therefore sec^2 theta - 1 = tan^2 theta

So, sec^2 theta ( sec^2 theta -1)
=( tan^2 theta +1) (tan^2 theta)
= tan^4 theta + tan^2 theta

Hence,proved.