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Question
If 0° < A < 90°; find A, if `(cos A )/(1 - sin A) + (cos A)/(1 + sin A) = 4`
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Solution
`(cos A )/(1 - sin A) + (cos A)/(1 + sin A) = 4`
`=> (cos A + cos A sin A + cos A - sin A cos A)/((1 - sin A)(1 + sin A)) = 4`
`=> (2 cos A)/(1 - sin^2 A) = 4`
`=> (2 cos A)/(cos^2 A) = 4`
`=> 1/cos A = 2`
`=> cos A = 1/2`
We know `cos 60^circ = 1/2`
Hence, A = 60°
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