Is tan² x = sec² x - 1 an identity?

We can prove the above identity by using other trigonometric identities.

Answer: tan² x = sec² x - 1 is an identity.

We can proceed step by step to prove this.

Explanation:

From trigonometric identities, sin² x + cos² x = 1

Dividing LHS and RHS of the above identity by cos² x, we get

(sin² x / cos² x) + (cos² x / cos² x) = 1 / cos² x ------(1)

Since, we know that sin² x / cos² x = tan² x and 1 / cos² x = sec² x 

Substituting these two value in equation (1), we get tan² x + 1 = sec² x 

tan² x = sec² x - 1 [ rearranging terms ]

Thus, tan² x = sec² x - 1 is an identity.