What is the value of sin(2arcsin((sqrt(3))/2)) ?

The value of sin(2arcsin((sqrt(3))/2)) is (sqrt(3))/2

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sin(2arcsin((sqrt(3))/2))

sin (2 arcsin (\frac{3}{2}))

\frac{3}{2}

Solution steps

sin (2 arcsin (\frac{3}{2}))

Rewrite using trig identities:

2 sin (arcsin (\frac{3}{2})) cos (arcsin (\frac{3}{2}))

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

Rewrite using trig identities:

sin (arcsin (\frac{3}{2})) = \frac{3}{2}

Rewrite using trig identities:

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

= 2 \cdot \frac{3}{2} \cdot \frac{1}{2}

Simplify

2 \cdot \frac{3}{2} \cdot \frac{1}{2} : \frac{3}{2}

= \frac{3}{2}

cos (arcsin (\frac{2}{5}))

\frac{sin ( 3 π )}{2}

- tan (1)

8 \cdot sin (6 0^{\circ})

arccos (\frac{5}{2})

What is the value of sin(2arcsin((sqrt(3))/2)) ?
The value of sin(2arcsin((sqrt(3))/2)) is (sqrt(3))/2