What is expand cos(θ)cot(θ)(sec(θ)-2tan(θ)) ?

The solution to expand cos(θ)cot(θ)(sec(θ)-2tan(θ)) is -2cot(θ)sin(θ)+cot(θ)

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expand cos(θ)cot(θ)(sec(θ)-2tan(θ))

expand

cos (θ) cot (θ) (sec (θ) - 2 tan (θ))

- 2 cot (θ) sin (θ) + cot (θ)

Solution steps

cos (θ) cot (θ) (sec (θ) - 2 tan (θ))

Apply the distributive law:

a (b - c) = ab - a c

cos (θ) cot (θ) (sec (θ) - 2 tan (θ)) = cos (θ) cot (θ) sec (θ) - cos (θ) cot (θ) \cdot 2 tan (θ)

= cos (θ) cot (θ) sec (θ) - cos (θ) cot (θ) \cdot 2 tan (θ)

Simplify

cos (θ) cot (θ) sec (θ) - cos (θ) cot (θ) \cdot 2 tan (θ) : cot (θ) (- 2 sin (θ) + 1)

= cot (θ) (- 2 sin (θ) + 1)

Apply the distributive law:

a (b + c) = ab + a c

cot (θ) (- 2 sin (θ) + 1) = cot (θ) (- 2 sin (θ)) + cot (θ) \cdot 1

= cot (θ) (- 2 sin (θ)) + cot (θ) \cdot 1

Simplify

cot (θ) (- 2 sin (θ)) + cot (θ) \cdot 1 : - 2 cot (θ) sin (θ) + cot (θ)

= - 2 cot (θ) sin (θ) + cot (θ)

tan (x) (1 - sin (2 x)) sec (x)

\frac{3 x}{sin ( x ) ( x - 3 )}

\frac{1}{4 ( 8 x + 12 )}

2 (\frac{y}{3} + 1)

(x - 10) (x + 5)

What is expand cos(θ)cot(θ)(sec(θ)-2tan(θ)) ?
The solution to expand cos(θ)cot(θ)(sec(θ)-2tan(θ)) is -2cot(θ)sin(θ)+cot(θ)