What is cos(arcsin(9x)) ?

The solution to cos(arcsin(9x)) is sqrt(1-81x^2)

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simplify cos(arcsin(9x))

simplify

cos (arcsin (9 x))

1 - 81 x^{2}

Solution steps

cos (arcsin (9 x))

Use the following identity:

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

= 1 - (9 x)^{2}

Simplify

= 1 - 81 x^{2}

cos (2 tan (- 1 (x)))

sec (\frac{π}{2} + x)

sin (- πn)

sec (arctan (2 x))

cos (\frac{3}{2} π + x)