What is the value of sin(2arctan(sqrt(2))) ?

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

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sin(2arctan(sqrt(2)))

sin (2 arctan (2))

\frac{2 2}{3}

Solution steps

sin (2 arctan (2))

Rewrite using trig identities:

2 sin (arctan (2)) cos (arctan (2))

= 2 sin (arctan (2)) cos (arctan (2))

Rewrite using trig identities:

sin (arctan (2)) = \frac{6}{3}

Rewrite using trig identities:

cos (arctan (2)) = \frac{3}{3}

= 2 \cdot \frac{6}{3} \cdot \frac{3}{3}

Simplify

2 \cdot \frac{6}{3} \cdot \frac{3}{3} : \frac{2 2}{3}

= \frac{2 2}{3}

\frac{tan ( 7 2 ^{\circ} ) - tan ( 1 2 ^{\circ} )}{1 + tan ( 7 2 ^{\circ} ) tan ( 1 2 ^{\circ} )}

arcsin (0.88)

0 csc (0)

10 sin (15 0^{\circ})

cos (6 5^{\circ}) + cos (5 5^{\circ})

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