What is ((sin^2(x)-cos^2(x)))/((tan^2(x)-1)) ?

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

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simplify ((sin^2(x)-cos^2(x)))/((tan^2(x)-1))

simplify

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

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

Solution steps

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

Use the Double Angle identity:

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

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

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

Apply the fraction rule:

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

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

(2 p + q)^{3} - (p + 2 q)^{3}

\frac{6 y ^{4} - 3 y ^{3}}{3 y ^{3}}

(3 x - 2) (2 x - 3) - x (6 x + 13)

(7 x + 3 y)^{3}

(u^{5})^{- 2}

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