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

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

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simplify cos(arcsin(2/x))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

cos (arcsin (\frac{8}{x}))

sin (2 π - x)

sin (9 0^{\circ} - θ)

sin (\frac{π}{2} - θ)

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