What is (1/2 (cos^2(x)-1))/(sin(x)tan(x)) ?

The solution to (1/2 (cos^2(x)-1))/(sin(x)tan(x)) is -1/2 sin(x)cot(x)

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simplify (1/2 (cos^2(x)-1))/(sin(x)tan(x))

simplify

\frac{\frac{1}{2} ( cos ^{2} ( x ) - 1 )}{sin ( x ) tan ( x )}

- \frac{1}{2} sin (x) cot (x)

Solution steps

\frac{\frac{1}{2} ( cos ^{2} ( x ) - 1 )}{sin ( x ) tan ( x )}

Simplify

\frac{1}{2} (cos^{2} (x) - 1) : - \frac{1}{2} sin^{2} (x)

= \frac{- \frac{1}{2} sin ^{2} ( x )}{sin ( x ) tan ( x )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

sin^{2} (x) = sin (x) sin (x)

= \frac{- \frac{1}{2} sin ( x ) sin ( x )}{sin ( x ) tan ( x )}

Cancel the common factor:

sin (x)

= \frac{- \frac{1}{2} sin ( x )}{tan ( x )}

Simplify

\frac{- \frac{1}{2} sin ( x )}{tan ( x )} : - \frac{1}{2} sin (x) cot (x)

= - \frac{1}{2} sin (x) cot (x)

r - 5 r - 6 s + 8 s - 15

1 \cdot 1 \cdot 1

(x (9 x^{2} + 6)^{\frac{1}{2}})^{2}

2 \cdot sin (x) \cdot cos (x)

What is (1/2 (cos^2(x)-1))/(sin(x)tan(x)) ?
The solution to (1/2 (cos^2(x)-1))/(sin(x)tan(x)) is -1/2 sin(x)cot(x)