Question

(sec θ + tan θ) (1 – sin θ) is equal to ______.

Options

• sin θ

• cos θ

• tan θ

• cot θ

Answer 1

(sec θ + tan θ) (1 – sin θ) is equal to cos θ.

Explanation:

sec θ = `1/cos θ`

`tan θ = sin θ/cos θ`

Substituting these into the first bracket:

`(1/cos θ + sin θ/cos θ) (1 - sin θ)`

`((1 + sin θ)/cos θ) (1 - sin θ)`

`((1 + sin θ) (1 - sin θ))/cos θ`

Using the Difference of Squares formula:

`(1^2 - sin^2 θ)/cos θ`

= `(1 - sin^2 θ)/cos θ`

Apply the Pythagorean Identity:

= `cos^2 θ/cos θ`

Divide cos² θ by cos θ

cos θ