What is cos(arcsin(x/2)) ?

The solution to cos(arcsin(x/2)) is (sqrt(4-x^2))/2

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simplify cos(arcsin(x/2))

simplify

cos (arcsin (\frac{x}{2}))

\frac{4 - x ^{2}}{2}

Solution steps

cos (arcsin (\frac{x}{2}))

Use the following identity:

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

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

Simplify

= \frac{4 - x ^{2}}{2}

cos (\frac{π}{2} - θ)

sin (x + \frac{π}{3})

sin (x + 2 π)

cos (x - 9 0^{\circ})

tan (x + π)