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

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

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

simplify

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

- csc^{2} (x)

Solution steps

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

Simplify

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

\frac{1}{sin ^{2} ( x )} : csc^{2} (x)

= - csc^{2} (x)

lo g_{5} (123)

7 + - 121

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

\frac{6}{8} + \frac{1}{4}

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