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

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

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

simplify

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

- sec^{2} (x)

Solution steps

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

Simplify

sec^{2} (x) - tan^{2} (x) : 1

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

\frac{1}{cos ^{2} ( x )} : sec^{2} (x)

= - sec^{2} (x)

5 \div 2 \frac{1}{3}

x^{10} - x^{2} y^{8}

\frac{1}{1 - 0.1}

160 \div 16

\frac{x - 2}{x - 3} - \frac{2 x - 2}{x - 3}

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