What is cot(arcsin(x/3)) ?

The solution to cot(arcsin(x/3)) is (sqrt(9-x^2))/x

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simplify cot(arcsin(x/3))

simplify

cot (arcsin (\frac{x}{3}))

\frac{9 - x ^{2}}{x}

Solution steps

cot (arcsin (\frac{x}{3}))

Use the following identity:

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

= \frac{1 - ( \frac{x}{3} ) ^{2}}{( \frac{x}{3} )}

Simplify

= \frac{9 - x ^{2}}{x}

tan (x - 18 0^{\circ})

cos (2 tan (- 1 x))

cot (arccot (x))

cos (\frac{π}{2} + θ)

2 cos (\frac{1}{2} x - 3) - 1