What is sin(arcsec(x/4)) ?

The solution to sin(arcsec(x/4)) is (sqrt(x^2-16))/x

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simplify sin(arcsec(x/4))

simplify

sin (arcsec (\frac{x}{4}))

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

Solution steps

sin (arcsec (\frac{x}{4}))

Use the following identity:

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

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

Simplify

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

cos (- t)

cos (x + \frac{π}{3})

sin (\frac{1}{sin ( x )})

cos (π - x) - sin (π - x)

2 cos (x - \frac{π}{3})