What is cos(arcsin(4/x)) ?

The solution to cos(arcsin(4/x)) is (sqrt(x^2-16))/x

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simplify cos(arcsin(4/x))

simplify

cos (arcsin (\frac{4}{x}))

\frac{x ^{2} - 16}{x}

Solution steps

cos (arcsin (\frac{4}{x}))

Use the following identity:

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

= 1 - (\frac{4}{x})^{2}

Simplify

= \frac{x ^{2} - 16}{x}

sin (arctan (\frac{x}{k}))

cos (18 0^{\circ} + x)

tan (\frac{π}{4} - x)

sin (arctan (\frac{x}{3}))

sin (18 0^{\circ} + x)