What is ((sin(x)-cos(x))/(cos(x)sin(x)))^{-2} ?

The solution to ((sin(x)-cos(x))/(cos(x)sin(x)))^{-2} is (cos^2(x)sin^2(x))/(-sin(2x)+1)

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simplify ((sin(x)-cos(x))/(cos(x)sin(x)))^{-2}

simplify

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

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

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(\frac{sin ( x ) - cos ( x )}{cos ( x ) sin ( x )})^{- 2} = \frac{1}{( \frac{s i n ( x ) - c o s ( x )}{c o s ( x ) s i n ( x )} ) ^{2}}

= \frac{1}{( \frac{s i n ( x ) - c o s ( x )}{c o s ( x ) s i n ( x )} ) ^{2}}

Simplify

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

= \frac{1}{\frac{( s i n ( x ) - c o s ( x ) ) ^{2}}{c o s ^{2} ( x ) s i n ^{2} ( x )}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

Simplify

(sin (x) - cos (x))^{2} : - sin (2 x) + 1

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

2.04 \cdot 1 0^{- 4}

(cos^{2} (x))^{3}

(1 - x) (1 - x)

(16 z^{4} y^{2}) (3 zy)

2.12 \cdot 1 0^{- 6}

What is ((sin(x)-cos(x))/(cos(x)sin(x)))^{-2} ?
The solution to ((sin(x)-cos(x))/(cos(x)sin(x)))^{-2} is (cos^2(x)sin^2(x))/(-sin(2x)+1)