What is (csc(x)-1)(csc(x)+1) ?

The solution to (csc(x)-1)(csc(x)+1) is cot^2(x)

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simplify (csc(x)-1)(csc(x)+1)

simplify

(csc (x) - 1) (csc (x) + 1)

cot^{2} (x)

Solution steps

(csc (x) - 1) (csc (x) + 1)

Express with sin, cos

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

Rewrite using trig identities

= cot^{2} (x)

\frac{8}{3}

\frac{b - 8}{b ^{2} - b - 6} - \frac{1}{3 - b}

- 2 x^{2} + 4

12 \cdot 43