What is expand sin(x)cos(x)(-csc(x)+sec(x)) ?

The solution to expand sin(x)cos(x)(-csc(x)+sec(x)) is -cot(x)sin(x)+sin(x)

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expand sin(x)cos(x)(-csc(x)+sec(x))

expand

sin (x) cos (x) (- csc (x) + sec (x))

- cot (x) sin (x) + sin (x)

Solution steps

sin (x) cos (x) (- csc (x) + sec (x))

= cos (x) sin (x) (- csc (x) + sec (x))

Apply the distributive law:

a (b + c) = ab + a c

cos (x) sin (x) (- csc (x) + sec (x)) = cos (x) sin (x) (- csc (x)) + cos (x) sin (x) sec (x)

= cos (x) sin (x) (- csc (x)) + cos (x) sin (x) sec (x)

Simplify

cos (x) sin (x) (- csc (x)) + cos (x) sin (x) sec (x) : sin (x) (- cot (x) + 1)

= sin (x) (- cot (x) + 1)

Apply the distributive law:

a (b + c) = ab + a c

sin (x) (- cot (x) + 1) = sin (x) (- cot (x)) + sin (x) \cdot 1

= sin (x) (- cot (x)) + sin (x) \cdot 1

Simplify

sin (x) (- cot (x)) + sin (x) \cdot 1 : - cot (x) sin (x) + sin (x)

= - cot (x) sin (x) + sin (x)

\frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})

(- 3 + 4 i)^{4}

(x^{3} - x + 30)^{5}

3 ((x^{2} - 5) - (3 x^{2} + 4) = x + 1)

What is expand sin(x)cos(x)(-csc(x)+sec(x)) ?
The solution to expand sin(x)cos(x)(-csc(x)+sec(x)) is -cot(x)sin(x)+sin(x)