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}

sec^{3} (\frac{π}{3})

tan (\frac{7 π}{6} - \frac{7 π}{4})

arctan (\frac{3}{5})

arcsin (csc (\frac{π}{2}))

cos (\frac{4 π}{7})

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