Question

Prove That;
(sin^4 theta - sec^2 theta) = tan^4 theta + tan^2 theta​

Answer 1

Answer:

Hi bro

Solution:

Given LHS = sec^{4}\theta -sec^{2}\theta

= sec^{2}\theta(sec^{2}\theta-1)

= (1+tan^{2}\theta)(1+tan^{2}\theta-1)

/* By Trigonometric identity:

sec²A = 1+tan²A */

= (1+tan^{2}\theta)\times tan^{2}\theta

=tan^{2}\theta+tan^{4}\theta

Rearranging the terms, we get

= tan^{4}\theta+tan^{2}\theta

= RHS