What is the value of cos(150)+sin(45)+1/2 cot(-330) ?

The value of cos(150)+sin(45)+1/2 cot(-330) is (sqrt(2))/2

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cos(150)+sin(45)+1/2 cot(-330)

cos (15 0^{\circ}) + sin (4 5^{\circ}) + \frac{1}{2} cot (- 33 0^{\circ})

\frac{2}{2}

Solution steps

cos (15 0^{\circ}) + sin (4 5^{\circ}) + \frac{1}{2} cot (- 33 0^{\circ})

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

Rewrite using trig identities:

cot (- 33 0^{\circ}) = 3

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

Simplify

- \frac{3}{2} + \frac{2}{2} + \frac{1}{2} 3 : \frac{2}{2}

= \frac{2}{2}

arctan (\frac{8 3}{- 8})

- e^{0} cos (0)

cos (6 \cdot π)

cos (15 5^{\circ}) cos (2 0^{\circ}) + sin (15 5^{\circ}) sin (2 0^{\circ})

sin (3) (\frac{π}{2})

What is the value of cos(150)+sin(45)+1/2 cot(-330) ?
The value of cos(150)+sin(45)+1/2 cot(-330) is (sqrt(2))/2