What is the value of arccos(1/2)+2arcsin(1/2) ?

The value of arccos(1/2)+2arcsin(1/2) is (2pi)/3

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arccos(1/2)+2arcsin(1/2)

arccos (\frac{1}{2}) + 2 arcsin (\frac{1}{2})

\frac{2 π}{3}

Solution steps

arccos (\frac{1}{2}) + 2 arcsin (\frac{1}{2})

Use the following trivial identity:

arccos (\frac{1}{2}) = \frac{π}{3}

Use the following trivial identity:

arcsin (\frac{1}{2}) = \frac{π}{6}

= \frac{π}{3} + 2 \cdot \frac{π}{6}

Simplify

\frac{π}{3} + 2 \cdot \frac{π}{6} : \frac{2 π}{3}

= \frac{2 π}{3}

\frac{tan ( 30 0 ^{\circ} )}{sin ( 12 0 ^{\circ} )}

cos (\frac{8 π}{7})

15 cos (5 0^{\circ})

arctan (\frac{2}{- 4})

4 + 3 cos (- \frac{π}{3})

What is the value of arccos(1/2)+2arcsin(1/2) ?
The value of arccos(1/2)+2arcsin(1/2) is (2pi)/3