What is sin(arcsec(x/2)) ?

The solution to sin(arcsec(x/2)) is (sqrt(x^2-4))/x

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simplify sin(arcsec(x/2))

simplify

sin (arcsec (\frac{x}{2}))

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

Solution steps

sin (arcsec (\frac{x}{2}))

Use the following identity:

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

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

Simplify

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

sin (θ + 9 0^{\circ})

tan (arccos (\frac{x}{8}))

tan (arccos (2 x))

4 cos (x + \frac{π}{3})

1 - (sin (x))^{2}