What is the value of sin(arccos(2/3)-arctan(1/2)) ?

The value of sin(arccos(2/3)-arctan(1/2)) is 2/3-(2sqrt(5))/(15)

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sin(arccos(2/3)-arctan(1/2))

sin (arccos (\frac{2}{3}) - arctan (\frac{1}{2}))

\frac{2}{3} - \frac{2 5}{15}

Solution steps

sin (arccos (\frac{2}{3}) - arctan (\frac{1}{2}))

Rewrite using trig identities:

sin (arccos (\frac{2}{3})) cos (arctan (\frac{1}{2})) - cos (arccos (\frac{2}{3})) sin (arctan (\frac{1}{2}))

= sin (arccos (\frac{2}{3})) cos (arctan (\frac{1}{2})) - cos (arccos (\frac{2}{3})) sin (arctan (\frac{1}{2}))

Rewrite using trig identities:

sin (arccos (\frac{2}{3})) = \frac{5}{3}

Rewrite using trig identities:

cos (arctan (\frac{1}{2})) = \frac{2 5}{5}

Rewrite using trig identities:

cos (arccos (\frac{2}{3})) = \frac{2}{3}

Rewrite using trig identities:

sin (arctan (\frac{1}{2})) = \frac{5}{5}

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

Simplify

\frac{5}{3} \cdot \frac{2 5}{5} - \frac{2}{3} \cdot \frac{5}{5} : \frac{2}{3} - \frac{2 5}{15}

= \frac{2}{3} - \frac{2 5}{15}

cos (7 5^{\circ}) cos (1 5^{\circ}) - sin (7 5^{\circ}) sin (1 5^{\circ})

\frac{22}{tan ( 1 2 ^{\circ} )}

cos (arctan (- \frac{2}{3}))

sin (3 0^{\circ}) \cdot 5

3 cos (\frac{5 π}{4})

What is the value of sin(arccos(2/3)-arctan(1/2)) ?
The value of sin(arccos(2/3)-arctan(1/2)) is 2/3-(2sqrt(5))/(15)