What is cot(θ)(1/(3cos(θ))+2/(cot(θ))-tan(θ)) ?

The solution to cot(θ)(1/(3cos(θ))+2/(cot(θ))-tan(θ)) is (cot(θ)+6cos(θ)-3sin(θ)cot(θ))/(3cos(θ))

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simplify cot(θ)(1/(3cos(θ))+2/(cot(θ))-tan(θ))

simplify

cot (θ) (\frac{1}{3 cos ( θ )} + \frac{2}{cot ( θ )} - tan (θ))

\frac{cot ( θ ) + 6 cos ( θ ) - 3 sin ( θ ) cot ( θ )}{3 cos ( θ )}

Solution steps

cot (θ) (\frac{1}{3 cos ( θ )} + \frac{2}{cot ( θ )} - tan (θ))

Join

\frac{1}{3 cos ( θ )} + \frac{2}{cot ( θ )} - tan (θ) : \frac{cot ( θ ) + 6 cos ( θ ) - 3 sin ( θ ) cot ( θ )}{3 cos ( θ ) cot ( θ )}

= cot (θ) \frac{cot ( θ ) + 6 cos ( θ ) - 3 sin ( θ ) cot ( θ )}{3 cos ( θ ) cot ( θ )}

Apply the fraction rule:

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

= \frac{cot ( θ ) ( cot ( θ ) + 6 cos ( θ ) - 3 sin ( θ ) cot ( θ ) )}{3 cos ( θ ) cot ( θ )}

Cancel the common factor:

cot (θ)

= \frac{cot ( θ ) + 6 cos ( θ ) - 3 sin ( θ ) cot ( θ )}{3 cos ( θ )}

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What is cot(θ)(1/(3cos(θ))+2/(cot(θ))-tan(θ)) ?
The solution to cot(θ)(1/(3cos(θ))+2/(cot(θ))-tan(θ)) is (cot(θ)+6cos(θ)-3sin(θ)cot(θ))/(3cos(θ))