Pre Calculus: Simplify this expression?

A

ADH

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Please simplify this expression:

(1-sin^2 X) / (sinX-cscX)

Please note that the numerator is NOT sin^2x ... the X is NOT included in the exponent.
 
(1 - sin^2 x) / (sinx - (1 / sinx))
(1 - sin^2 x) / ((sin^2 x /sin x) - (1/sin x))
(1 - sin^2 x) / ((sin^2 x - 1) / sin x)
(1 - sin^2 x) / -((1 - sin^2 x) / sin x)
(1 - sin^2 x) / ((1 - sin^2 x) / -sin x)
(1 - sin^2 x) * (-sin x / (1 - sin^2 x))
-sinx x
 
(1 - sin^2 x) / (sinx - (1 / sinx))
(1 - sin^2 x) / ((sin^2 x /sin x) - (1/sin x))
(1 - sin^2 x) / ((sin^2 x - 1) / sin x)
(1 - sin^2 x) / -((1 - sin^2 x) / sin x)
(1 - sin^2 x) / ((1 - sin^2 x) / -sin x)
(1 - sin^2 x) * (-sin x / (1 - sin^2 x))
-sinx x
 
(1 - sin(x)^2) / (sin(x) - csc(x))
= cos(x)^2 / (sin(x) - csc(x))
= cos(x)^2 / ((sin(x)^2 / sin(x)) - csc(x))
= cos(x)^2 / ((sin(x)^2 / sin(x)) - (1 / sin(x)))
= cos(x)^2 / ((sin(x)^2 - 1) / sin(x))
= cos(x)^2 / (-(1 - sin(x)^2) / sin(x))
= cos(x)^2 / (-cos(x)^2 / sin(x))
= cos(x)^2 * (sin(x) / -cos(x)^2)
= cos(x)^2 * (-sin(x) / cos(x)^2)
= -sin(x)
 
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