What is expand-(cos(θ)(-cos(θ)+2)-sin^2(θ))/(2sin(θ)) ?

The solution to expand-(cos(θ)(-cos(θ)+2)-sin^2(θ))/(2sin(θ)) is -(cos(θ))/(sin(θ))+1/(2sin(θ))

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expand-(cos(θ)(-cos(θ)+2)-sin^2(θ))/(2sin(θ))

expand

- \frac{cos ( θ ) ( - cos ( θ ) + 2 ) - sin ^{2} ( θ )}{2 sin ( θ )}

- \frac{cos ( θ )}{sin ( θ )} + \frac{1}{2 sin ( θ )}

Solution steps

- \frac{cos ( θ ) ( - cos ( θ ) + 2 ) - sin ^{2} ( θ )}{2 sin ( θ )}

Expand

cos (θ) (- cos (θ) + 2) - sin^{2} (θ) : - cos^{2} (θ) + 2 cos (θ) - sin^{2} (θ)

= - \frac{2 cos ( θ ) - cos ^{2} ( θ ) - sin ^{2} ( θ )}{2 sin ( θ )}

Simplify

- cos^{2} (θ) + 2 cos (θ) - sin^{2} (θ) : 2 cos (θ) - 1

= - \frac{2 cos ( θ ) - 1}{2 sin ( θ )}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{2 cos ( θ ) - 1}{2 sin ( θ )} = - (\frac{2 cos ( θ )}{2 sin ( θ )}) - (- \frac{1}{2 sin ( θ )})

= - (\frac{2 cos ( θ )}{2 sin ( θ )}) - (- \frac{1}{2 sin ( θ )})

Remove parentheses:

(a) = a, - (- a) = a

= - \frac{2 cos ( θ )}{2 sin ( θ )} + \frac{1}{2 sin ( θ )}

Divide the numbers:

\frac{2}{2} = 1

= - \frac{cos ( θ )}{sin ( θ )} + \frac{1}{2 sin ( θ )}

x^{2} - 2 x (x^{3} + 7 x^{4} - 23 x^{2} - 10 x) d x

(2 x + 5)^{2}

x (x + 3)^{2}

22 (33 + 57)

- \frac{d}{d x} ((b + 2 c m) \cdot e^{- y x})

What is expand-(cos(θ)(-cos(θ)+2)-sin^2(θ))/(2sin(θ)) ?
The solution to expand-(cos(θ)(-cos(θ)+2)-sin^2(θ))/(2sin(θ)) is -(cos(θ))/(sin(θ))+1/(2sin(θ))