#### Question

Prove the following trigonometric identities.

(secθ + cosθ) (secθ − cosθ) = tan^{2}θ + sin^{2}θ

#### Solution

We have to prove`(sec theta + cos theta)(sec theta - cos theta) = tan^2 theta + sin^2 theta`

We know that

`sin^2 theta + cos^2 theta = 1`

`sec^2 theta - tan^2 theta = 1`

`(sec theta + cos theta)(sec theta - cos theta) = sec^2 theta - cos^2 theta`

`= (1 + tan^2 theta) - (1 - sin^2 theta)`

`= 1 + tan^2 theta - 1 + sin^2 theta`

`= tan^2 theta + sin^2 theta`

Is there an error in this question or solution?

#### APPEARS IN

Solution Prove the Following Trigonometric Identities. (Secθ + Cosθ) (Secθ − Cosθ) = Tan2θ + Sin2θ Concept: Trigonometric Ratios of Complementary Angles.