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

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

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sin(2arccos((sqrt(2))/2))

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

1

Solution steps

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

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

= 1

arccos (\frac{17}{28})

4 sec^{2} (1 8^{\circ}) - 4 tan^{2} (1 8^{\circ})

3 sin (\frac{π}{4}) + 3 cos (\frac{π}{4})

tan (\frac{- π}{2})

2 cos (\frac{π}{6}) + sin (2 (\frac{π}{6}))

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