What is cos(arcsin(ax)) ?

The solution to cos(arcsin(ax)) is sqrt(1-a^2x^2)

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simplify cos(arcsin(ax))

simplify

cos (arcsin (a x))

1 - a^{2} x^{2}

Solution steps

cos (arcsin (a x))

Use the following identity:

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

= 1 - (a x)^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 1 - a^{2} x^{2}

- 2 cos (3 x - \frac{π}{2})

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

tan (arccos (\frac{x}{5}))

1 + (tan (x))^{2}

sin (- x) + sin (x)