What is the value of sin(2arcsin(1/2)) ?

The value of sin(2arcsin(1/2)) is (sqrt(3))/2

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sin(2arcsin(1/2))

sin (2 arcsin (\frac{1}{2}))

\frac{3}{2}

Solution steps

sin (2 arcsin (\frac{1}{2}))

Rewrite using trig identities:

2 sin (arcsin (\frac{1}{2})) cos (arcsin (\frac{1}{2}))

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

Rewrite using trig identities:

sin (arcsin (\frac{1}{2})) = \frac{1}{2}

Rewrite using trig identities:

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

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

Simplify

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

= \frac{3}{2}

tan (- \frac{13 π}{4})

- csc^{2} (\frac{3 π}{4})

arcsin (\frac{2}{π})

sin (69 0^{\circ})

sin^{2} (5 5^{\circ})

What is the value of sin(2arcsin(1/2)) ?
The value of sin(2arcsin(1/2)) is (sqrt(3))/2