What is 1/(sqrt(csc^2(x)-1)) ?

The solution to 1/(sqrt(csc^2(x)-1)) is tan(x)

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simplify 1/(sqrt(csc^2(x)-1))

simplify

\frac{1}{csc ^{2} ( x ) - 1}

tan (x)

Solution steps

\frac{1}{csc ^{2} ( x ) - 1}

Use the Pythagorean identity:

csc^{2} (x) = 1 + cot^{2} (x)

csc^{2} (x) - 1 = cot^{2} (x)

= \frac{1}{cot ^{2} ( x )}

cot^{2} (x) = cot (x)

= \frac{1}{cot ( x )}

Rewrite using trig identities

= tan (x)

cos (x - \frac{11 π}{6})

cos (2 θ - \frac{π}{4})

a sin (- \frac{1}{2} ka)

2 sin (2 x - \frac{π}{6}) + 2

arctan (- \frac{1}{tan ( ω t )})