Verify the identify Simplify at each step tan4 x tan2 x sec

Verify the identify. (Simplify at each step.) tan^4 x = tan^2 x sec^2 x - tan^2 x tan^4 x = (tan^2 x) = (tan^2 x) tan^2 x sec^2 - tan^2 x

Solution

Solution:

Given

tan⁴x = tan²x sec²x - tan²x

= tan²x sec²x - tan²x

=  - tan²x + (1+ tan²x) tan²x)

=  - tan²x + tan²x tan²x + tan²x

= - tan²x + tan⁴x + tan²x

= tan⁴x

True

Therefore

tan⁴x = tan²x sec²x - tan²x