Question

Verify the identity
sec^2(x)tan^2(x)+sec^2(x)=sec^4(x)

Answer 1

see explanation

Explanation:

Using the trigonometric identity

tan²x + 1 = sec²x ⇒ tan²x = sec²x - 1

Consider the left side

sec²x × tan²x + sec²x

= sec²x(sec²x - 1) + sec²x ← distribute and simplify

=
`sec^(4)` x - sec²x + sec²x

=
`sec^(4)` x = right side ⇒ verified