Question

Prove the identity sec^2 x * tan^2 + sec^2 x = sec ^4 x. show all work.

Answer 1

see explanation

Explanation:

using the trigonometric identity

• tan²x + 1 = sec²x

consider the left side

sec²x × tan²x + sec²x ← factor out sec²x from each term

= sec²x( tan²x + 1)

= sec²x (sec²x )

=
`sec^(4)`x

= right side , thus proven