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

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

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

simplify

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

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

Solution steps

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

Simplify

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

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

Apply exponent rule:

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

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

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

Cancel the common factor:

sin (a)

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

Simplify

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

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

\frac{2}{x - 4} + \frac{3}{x + 7}

(8 x + 3)^{2}

lo g_{7} (x^{3}) - lo g_{7} (x)

\frac{4 - 4 i}{8 i}

\frac{1}{800} \div \frac{1}{32000}

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