What is sin(arcsin(x)+pi/6) ?

The solution to sin(arcsin(x)+pi/6) is (sqrt(3)x+sqrt(1-x^2))/2

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simplify sin(arcsin(x)+pi/6)

simplify

sin (arcsin (x) + \frac{π}{6})

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

Solution steps

sin (arcsin (x) + \frac{π}{6})

Rewrite using trig identities

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

Use the following identity:

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

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

Use the following identity:

sin (arcsin (x)) = x

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

Simplify

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

csc (\frac{π}{2} - x)

9 sin^{2} (- 16 cos^{2} (x))

tan (27 0^{\circ} + B)

5 sin (\frac{π}{6} + x)

tan (\cdot arctan (x))

What is sin(arcsin(x)+pi/6) ?
The solution to sin(arcsin(x)+pi/6) is (sqrt(3)x+sqrt(1-x^2))/2