Question

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

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)].