Simplify (1-sin^2x) / (sinx-cscx)

Question

Marlee Chang

Mathematics

30 July, 07:34

Simplify (1-sin^2x) / (sinx-cscx)

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Alyson Fitzgerald · Answer 1

1 - sin ^2 (x) / sin (x) - cosec (x) = Cos^2 (x) / [ sin (x) - 1/sin (x) ] {since sin^2 (x) + cos ^2 (x) = 1 and cosec (x) = 1/sin (x) }. Therefore cos^2 (x) / [sin^2 (x) - 1] = Cos^2 (x). Sin (x) / [ - cos^2 (x) ] {since, sin^2 (x) - 1 = cos^2 (x) } = - sin (x). So answer is [-sin (x) ].