Question

Which of the following is true?

Options

• sec² θ + tan² θ = 1

• sec² θ = tan² θ − 1

• sec² θ = 1 + tan² θ

• tan² θ = 2 − sec² θ

Answer 1

sec² θ = 1 + tan² θ

Explanation:

sin² θ + cos² θ = 1

Divide every term by cos² θ.

`sin^2 θ/cos^2 θ + cos^2 θ/cos^2 θ`

= `1/cos^2 θ`

Apply the Quotient and Reciprocal Identities:

`sin^2 θ/cos^2 θ = tan^2 θ`

`cos^2 θ/cos^2 θ = 1`

`1/cos^2 θ = sec^2 θ`