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Question
`(tanA + secA - 1)/(tanA - secA + 1)` = ______
Options
`(1 - sinA)/cosA`
`(1 - cosA)/sinA`
`(1 + sinA)/cosA`
`(1 + cosA)/sinA`
MCQ
Fill in the Blanks
Solution
`(tanA + secA - 1)/(tanA - secA + 1)` = `underline((1 + sinA)/cosA)`
Explanation:
`(tanA + secA - 1)/(tanA - secA + 1)` = `(sinA + 1 - cosA)/(sinA - 1 + cosA)`
= `(sinA + (1 - cosA))/(sinA - (1 - cosA))`
= `(2sin A/2 cos A/2 + 2sin^2 A/2)/(2sin A/2 cos A/2 - 2sin^2 A/2)`
= `(cos A/2 + sin A/2)/(cos A/2 - sin A/2)`
= `(cos A/2 + sin A/2)^2/(cos^2 A/2 - sin^2 A/2)`
= `(1 + sinA)/cosA`
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Trigonometric Functions of Sum and Difference of Angles
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