What is expand (50cos(8x))/((cos(x)-1)^2) ?

The solution to expand (50cos(8x))/((cos(x)-1)^2) is (50cos(8x))/(cos^2(x)-2cos(x)+1)

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expand (50cos(8x))/((cos(x)-1)^2)

expand

\frac{50 cos ( 8 x )}{( cos ( x ) - 1 ) ^{2}}

\frac{50 cos ( 8 x )}{cos ^{2} ( x ) - 2 cos ( x ) + 1}

Solution steps

\frac{50 cos ( 8 x )}{( cos ( x ) - 1 ) ^{2}}

(cos (x) - 1)^{2} = cos^{2} (x) - 2 cos (x) + 1

= \frac{50 cos ( 8 x )}{cos ^{2} ( x ) - 2 cos ( x ) + 1}

\frac{a}{z ( z + b )}

2 ((- 2 x + 2) (2 x^{2} - 1))

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

\frac{x ^{2} - 6 x + 2}{( x - 3 ) ^{2}}

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

What is expand (50cos(8x))/((cos(x)-1)^2) ?
The solution to expand (50cos(8x))/((cos(x)-1)^2) is (50cos(8x))/(cos^2(x)-2cos(x)+1)