What is expand-csc(x)(sin(4x)-2sin(3x)cos(x)) ?

The solution to expand-csc(x)(sin(4x)-2sin(3x)cos(x)) is 2cot(x)sin(3x)-csc(x)sin(4x)

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expand-csc(x)(sin(4x)-2sin(3x)cos(x))

expand

- csc (x) (sin (4 x) - 2 sin (3 x) cos (x))

2 cot (x) sin (3 x) - csc (x) sin (4 x)

Solution steps

- csc (x) (sin (4 x) - 2 sin (3 x) cos (x))

Apply the distributive law:

a (b - c) = ab - a c

- csc (x) (sin (4 x) - 2 sin (3 x) cos (x)) = - csc (x) sin (4 x) - (- csc (x)) \cdot 2 sin (3 x) cos (x)

= - csc (x) sin (4 x) - (- csc (x)) \cdot 2 sin (3 x) cos (x)

Simplify

- csc (x) sin (4 x) - (- csc (x)) \cdot 2 sin (3 x) cos (x) : 2 cot (x) sin (3 x) - csc (x) sin (4 x)

= 2 cot (x) sin (3 x) - csc (x) sin (4 x)

\frac{12 x ^{3}}{3 x}

2 (e^{5} - 1)

25 (- 46 + 4)

\frac{( 7 x - 2 ) ^{n}}{( n + 3 ) ^{2}}

(r cos (x) - r sin (x))^{2}

What is expand-csc(x)(sin(4x)-2sin(3x)cos(x)) ?
The solution to expand-csc(x)(sin(4x)-2sin(3x)cos(x)) is 2cot(x)sin(3x)-csc(x)sin(4x)