What is expand (2sec^2(x))/((tan(x)-1)^2) ?

The solution to expand (2sec^2(x))/((tan(x)-1)^2) is 2/(1-sin(2x))

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expand (2sec^2(x))/((tan(x)-1)^2)

expand

\frac{2 sec ^{2} ( x )}{( tan ( x ) - 1 ) ^{2}}

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

Solution steps

\frac{2 sec ^{2} ( x )}{( tan ( x ) - 1 ) ^{2}}

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

= \frac{2 sec ^{2} ( x )}{tan ^{2} ( x ) - 2 tan ( x ) + 1}

Express with sin, cos

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

Rewrite using trig identities

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

\frac{- x ^{2} + 2 x - 5}{( x + 1 ) ( x ^{2} + 6 x + 9 )}

\frac{10 s - 15}{( 1 + s ) ( 2 s + 1 )}

\frac{3 ( 3 ^{k} - 1 )}{2}

\frac{x - 6}{x ( x + 6 )}

\frac{( 4 x - 1 ) ^{3}}{64}

What is expand (2sec^2(x))/((tan(x)-1)^2) ?
The solution to expand (2sec^2(x))/((tan(x)-1)^2) is 2/(1-sin(2x))