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

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

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

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

1

Solution steps

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

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

= 1

tan (\frac{7}{24})

cos (\frac{3}{π})

arctan (\frac{- 3}{0})

\frac{3 cos ( π )}{sin ( π ) + 6}

arccos (10)

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