What is the value of sin(2arctan(8/15)) ?

The value of sin(2arctan(8/15)) is 240/289

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sin(2arctan(8/15))

sin (2 arctan (\frac{8}{15}))

\frac{240}{289}

Solution steps

sin (2 arctan (\frac{8}{15}))

Rewrite using trig identities:

2 sin (arctan (\frac{8}{15})) cos (arctan (\frac{8}{15}))

= 2 sin (arctan (\frac{8}{15})) cos (arctan (\frac{8}{15}))

Rewrite using trig identities:

sin (arctan (\frac{8}{15})) = \frac{8}{17}

Rewrite using trig identities:

cos (arctan (\frac{8}{15})) = \frac{15}{17}

= 2 \cdot \frac{8}{17} \cdot \frac{15}{17}

Simplify

2 \cdot \frac{8}{17} \cdot \frac{15}{17} : \frac{240}{289}

= \frac{240}{289}

cos (\frac{3 π}{16})

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

4 + 4 cos (\frac{π}{2})

20 \cdot sin (12 0^{\circ})

sin (61.9 3^{\circ})

What is the value of sin(2arctan(8/15)) ?
The value of sin(2arctan(8/15)) is 240/289