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Question
`(sinA.tanA)/(1 - cos A) - 1` is equal to ______.
Options
cosec А
sec A
sin A
tan A
MCQ
Fill in the Blanks
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Solution
`(sinA.tanA)/(1 - cos A) - 1` is equal to sec A.
Explanation:
We know,
tan A = `sin A/cos A`
`(sin A.(sin A/cos A))/(1 - cos A) - 1`
`(sin^2 A/cos A)/(1 - cos A) - 1`
cos A from the numerator to the denominator:
`sin^2 A/(cos A(1 - cos A)) - 1`
`(1 + cos A)/cos A- 1`
`(1/ cos A + cos A/cos A) - 1`
sec A + 1 − 1
sec A
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