What is sin(arcsin(x)+pi/3) ?

The solution to sin(arcsin(x)+pi/3) is (x+sqrt(3)sqrt(1-x^2))/2

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simplify sin(arcsin(x)+pi/3)

simplify

sin (arcsin (x) + \frac{π}{3})

\frac{x + 3 1 - x ^{2}}{2}

Solution steps

sin (arcsin (x) + \frac{π}{3})

Rewrite using trig identities

= \frac{1}{2} sin (arcsin (x)) + \frac{3}{2} cos (arcsin (x))

Use the following identity:

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

= \frac{1}{2} sin (arcsin (x)) + \frac{3}{2} 1 - x^{2}

Use the following identity:

sin (arcsin (x)) = x

= \frac{1}{2} x + \frac{3}{2} 1 - x^{2}

Simplify

= \frac{x + 3 1 - x ^{2}}{2}

sin (x - \frac{π}{3})

ln (sec (θ)) + ln (cos (θ))

sin (3 x - \frac{π}{3})

cos (θ + π)

cos (arcsin (6 x))

What is sin(arcsin(x)+pi/3) ?
The solution to sin(arcsin(x)+pi/3) is (x+sqrt(3)sqrt(1-x^2))/2