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.
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.