Question

(sec A + tan A) (1 − sin A) = ______.

Options

• sec A

• sin A

• cosec A

• cos A

Answer 1

(sec A + tan A) (1 − sin A) = cos A.

Explanation:

The given expression is `(sec "A"+tan "A") (1-sin "A")`.

Simplifying the given expression, we have

`(sec "A"+tan "A")(1-sin "A")`

= `(1/cos "A"+sin "A"/cos "A")(1-sin "A")`

= `(1+sin "A")/(cos"A")xx(1-sin "A")`

= `((1+sin "A")(1-sin "A"))/(cos "A")`

= `(1-sin^2 "A")/cos "A"` 

= `cos^2 "A"/cos "A"`

= `cos "A"`