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

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

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sin(2arccos(1/2))

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

\frac{3}{2}

Solution steps

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

sin (arccos (\frac{1}{2})) = \frac{3}{2}

Rewrite using trig identities:

cos (arccos (\frac{1}{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}

1 - 2 sin^{2} (7 5^{\circ})

30 \cdot cos (3 0^{\circ})

0 - cos (0)

cos (\frac{2}{π})

tan (arccos (\frac{1}{5}))

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