What is expand ((-cos(y)(2xsin(y)-cos(x)))-1)/x ?

The solution to expand ((-cos(y)(2xsin(y)-cos(x)))-1)/x is -1/x+(cos(y)cos(x))/x-sin(2y)

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expand ((-cos(y)(2xsin(y)-cos(x)))-1)/x

expand

\frac{( - cos ( y ) ( 2 x sin ( y ) - cos ( x ) ) ) - 1}{x}

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

Solution steps

\frac{( - cos ( y ) ( 2 x sin ( y ) - cos ( x ) ) ) - 1}{x}

Remove parentheses:

(- a) = - a

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

Expand

- cos (y) (2 x sin (y) - cos (x)) - 1 : - 2 x cos (y) sin (y) + cos (y) cos (x) - 1

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

Simplify

- 2 x cos (y) sin (y) + cos (y) cos (x) - 1 : cos (y) cos (x) - x sin (2 y) - 1

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

Apply the fraction rule:

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

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

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

Cancel

\frac{sin ( 2 y ) x}{x} : sin (2 y)

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

\frac{( 7 x + 8 ) ( 6 x + 4 )}{( x ^{2} - 16 ) ^{2}}

\frac{3 x}{( x - 2 ) ( x - 1 )}

\frac{1.2538 ( 1 + 0.16 s ) ( 1 + 0.16 s )}{s}

\frac{- 2 s ^{2} - 3 s - 11}{( s - 1 ) ( s + 2 ) ( s - 3 )}

\frac{( x - 6 ) ^{2}}{6 - 5 x}

What is expand ((-cos(y)(2xsin(y)-cos(x)))-1)/x ?
The solution to expand ((-cos(y)(2xsin(y)-cos(x)))-1)/x is -1/x+(cos(y)cos(x))/x-sin(2y)