Learn Is Tan 2x Sec 2x 1 An Identity

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# Is tan^{2 }x = sec^{2 }x - 1 an identity?

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

## Answer: tan^{2 }x = sec^{2 }x - 1 is an identity.

We can proceed step by step to prove this.

**Explanation:**

From trigonometric identities, sin^{2 }x + cos^{2 }x = 1

Dividing LHS and RHS of the above identity by cos^{2 }x, we get

(sin^{2 }x / cos^{2 }x) + (cos^{2 }x / cos^{2 }x) = 1 / cos^{2 }x ------(1)

Since, we know that sin^{2 }x / cos^{2 }x = tan^{2 }x and 1 / cos^{2 }x = sec^{2} x

Substituting these two value in equation (1), we get tan^{2 }x + 1 = sec^{2} x

tan^{2 }x = sec^{2} x - 1 [ rearranging terms ]

### Thus, tan^{2 }x = sec^{2} x - 1 is an identity.

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