What is the value of csc((2pi)/3)-cos((5pi)/4)+sin(pi/6) ?

The value of csc((2pi)/3)-cos((5pi)/4)+sin(pi/6) is (4sqrt(3)+3+3sqrt(2))/6

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csc((2pi)/3)-cos((5pi)/4)+sin(pi/6)

csc (\frac{2 π}{3}) - cos (\frac{5 π}{4}) + sin (\frac{π}{6})

\frac{4 3 + 3 + 3 2}{6}

Solution steps

csc (\frac{2 π}{3}) - cos (\frac{5 π}{4}) + sin (\frac{π}{6})

Rewrite using trig identities:

csc (\frac{2 π}{3}) = \frac{2 3}{3}

Rewrite using trig identities:

cos (\frac{5 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

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

Simplify

\frac{2 3}{3} - (- \frac{2}{2}) + \frac{1}{2} : \frac{4 3 + 3 + 3 2}{6}

= \frac{4 3 + 3 + 3 2}{6}

tan (27 π)

sin (arccos (- \frac{9}{145}))

\frac{1}{cos ( 9 0 ^{\circ} )}

- e^{0} sin (2)

\frac{sin ( 6 0 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

What is the value of csc((2pi)/3)-cos((5pi)/4)+sin(pi/6) ?
The value of csc((2pi)/3)-cos((5pi)/4)+sin(pi/6) is (4sqrt(3)+3+3sqrt(2))/6