What is the value of sin(2arctan(5/12)) ?

The value of sin(2arctan(5/12)) is 120/169

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sin(2arctan(5/12))

sin (2 arctan (\frac{5}{12}))

\frac{120}{169}

Solution steps

sin (2 arctan (\frac{5}{12}))

Rewrite using trig identities:

2 sin (arctan (\frac{5}{12})) cos (arctan (\frac{5}{12}))

= 2 sin (arctan (\frac{5}{12})) cos (arctan (\frac{5}{12}))

Rewrite using trig identities:

sin (arctan (\frac{5}{12})) = \frac{5}{13}

Rewrite using trig identities:

cos (arctan (\frac{5}{12})) = \frac{12}{13}

= 2 \cdot \frac{5}{13} \cdot \frac{12}{13}

Simplify

2 \cdot \frac{5}{13} \cdot \frac{12}{13} : \frac{120}{169}

= \frac{120}{169}

tan (\frac{135}{2})

csc (7)

arccos (\frac{4.4}{6.5})

cos (arctan (- 7))

arccos (sin (- \frac{5 π}{3}))

What is the value of sin(2arctan(5/12)) ?
The value of sin(2arctan(5/12)) is 120/169