What is (-cot(x)sin(x)+cos^3(x))/(sin(x)-cot(x)) ?

The solution to (-cot(x)sin(x)+cos^3(x))/(sin(x)-cot(x)) is (-cos(x)+cos^3(x))/(sin(x)-cot(x))

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simplify (-cot(x)sin(x)+cos^3(x))/(sin(x)-cot(x))

simplify

\frac{- cot ( x ) sin ( x ) + cos ^{3} ( x )}{sin ( x ) - cot ( x )}

\frac{- cos ( x ) + cos ^{3} ( x )}{sin ( x ) - cot ( x )}

Solution steps

\frac{- cot ( x ) sin ( x ) + cos ^{3} ( x )}{sin ( x ) - cot ( x )}

Use the basic trigonometric identity:

cot (x) = \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )} sin (x)

Simplify

\frac{cos ( x )}{sin ( x )} sin (x) : cos (x)

= \frac{- cos ( x ) + cos ^{3} ( x )}{sin ( x ) - cot ( x )}

(5 k + 4 m)^{3}

2 x + 2 - 2 x

a^{4} - 81 b^{10}

\frac{( e ^{n} )}{( e ^{2 n} + g )}

\frac{( ( x ^{3} + 4 x ^{2} ) ( 2 x + 4 ) )}{( 2 x ^{2} + 12 x + 16 )}

What is (-cot(x)sin(x)+cos^3(x))/(sin(x)-cot(x)) ?
The solution to (-cot(x)sin(x)+cos^3(x))/(sin(x)-cot(x)) is (-cos(x)+cos^3(x))/(sin(x)-cot(x))