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Question
(sec A + tan A) (1 − sin A) = ______.
Options
sec A
sin A
cosec A
cos A
Solution
(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"`
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