What is the value of sin(2arctan(4/3)) ?

The value of sin(2arctan(4/3)) is 24/25

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sin(2arctan(4/3))

sin (2 arctan (\frac{4}{3}))

\frac{24}{25}

Solution steps

sin (2 arctan (\frac{4}{3}))

Rewrite using trig identities:

2 sin (arctan (\frac{4}{3})) cos (arctan (\frac{4}{3}))

= 2 sin (arctan (\frac{4}{3})) cos (arctan (\frac{4}{3}))

Rewrite using trig identities:

sin (arctan (\frac{4}{3})) = \frac{4}{5}

Rewrite using trig identities:

cos (arctan (\frac{4}{3})) = \frac{3}{5}

= 2 \cdot \frac{4}{5} \cdot \frac{3}{5}

Simplify

2 \cdot \frac{4}{5} \cdot \frac{3}{5} : \frac{24}{25}

= \frac{24}{25}

sin (21 5^{\circ})

9 sin (\frac{2 π}{3})

6 cos (π)

sin (2 arcsin (\frac{7}{25}))

tan (arctan (\frac{7}{3}))

What is the value of sin(2arctan(4/3)) ?
The value of sin(2arctan(4/3)) is 24/25