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

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

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sin(2arctan(3/4))

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

\frac{24}{25}

Solution steps

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

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

= \frac{24}{25}

cos^{2} (\frac{π}{12}) - sin^{2} (\frac{π}{12})

sin (π (1))

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

\frac{10}{sin ( 5 5 ^{\circ} )}

sin (\frac{π}{11})

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