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Verify the trigonometric identity  square root [(1+sin x)/(1-sinx)]=(1+sinx)/|cosx|

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We have to verify: sqrt [(1 + sin x)/(1 - sin x)] = (1 + sin x)/|cos x|

sqrt [(1 + sin x)/(1 - sin x)]

=> sqrt [(1 + sin x)(1 + sin x)/(1 - sin x)(1 + sin x)]

=> sqrt [(1 + sin x)^2/(1 - (sin x)^2)]

=> sqrt [(1 + sin x)^2/(cos x)^2]

=> (1 + sin x)/|cos x|

This verifies that sqrt [(1 + sin x)/(1 - sin x)] = (1 + sin x)/|cos x|