What is cos(arcsin(x/9)) ?

The solution to cos(arcsin(x/9)) is (sqrt(81-x^2))/9

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simplify cos(arcsin(x/9))

simplify

cos (arcsin (\frac{x}{9}))

\frac{81 - x ^{2}}{9}

Solution steps

cos (arcsin (\frac{x}{9}))

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

= 1 - (\frac{x}{9})^{2}

Simplify

= \frac{81 - x ^{2}}{9}

cos (2 (- x))

cos (2 x - \frac{5 π}{6})

4 sin (\frac{π}{6} + x) - cos (x)

- cos (\frac{π}{3} + x)

(4 tan (θ))^{2} + 16