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

The value of sin(arccos(-2/3)+2arctan(-1/3)) is sin(arccos(-2/3)-2arctan(1/3))

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

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

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

Decimal Notation

0.99628 \dots

Solution steps

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

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{1}{3}) = - arctan (\frac{1}{3})

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

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

sin (arcsin (\frac{5}{13}) + arcsin (\frac{4}{5}))

cosh (ln (1 + 2 i))

sin (arctan (\frac{5}{12}) + arccos (\frac{7}{25}))

tan (- 81 0^{\circ})

arccos (sec (π))

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