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

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

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arcsin((sqrt(3))/2)+arccos(1/2)

arcsin (\frac{3}{2}) + arccos (\frac{1}{2})

\frac{2 π}{3}

Solution steps

arcsin (\frac{3}{2}) + arccos (\frac{1}{2})

Use the following trivial identity:

arcsin (\frac{3}{2}) = \frac{π}{3}

Use the following trivial identity:

arccos (\frac{1}{2}) = \frac{π}{3}

= \frac{π}{3} + \frac{π}{3}

Simplify

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

= \frac{2 π}{3}

sec (arctan (\frac{6}{7}))

- cos (4 π)

sin (\frac{π}{3}) cos (\frac{π}{7}) - sin (\frac{π}{7}) cos (\frac{π}{3})

4 sec^{2} (0)

csc (\frac{- 5 π}{6})

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