What is the value of sqrt(3)sin(pi/3)-1/2 cos^2(pi/3)-7/8 ?

The value of sqrt(3)sin(pi/3)-1/2 cos^2(pi/3)-7/8 is 1/2

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sqrt(3)sin(pi/3)-1/2 cos^2(pi/3)-7/8

3 sin (\frac{π}{3}) - \frac{1}{2} cos^{2} (\frac{π}{3}) - \frac{7}{8}

\frac{1}{2}

Solution steps

3 sin (\frac{π}{3}) - \frac{1}{2} cos^{2} (\frac{π}{3}) - \frac{7}{8}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

= 3 \frac{3}{2} - \frac{1}{2} (\frac{1}{2})^{2} - \frac{7}{8}

Simplify

3 \frac{3}{2} - \frac{1}{2} (\frac{1}{2})^{2} - \frac{7}{8} : \frac{1}{2}

= \frac{1}{2}

cos (\frac{3 π}{4}) + i \cdot sin (\frac{3 π}{4})

cos^{3} (9 0^{\circ})

4 + \frac{3 2}{2} cos (\frac{3 π}{4})

\frac{1}{cos ^{2} ( \frac{π}{3} )}

arccos (\frac{5}{9 14})

What is the value of sqrt(3)sin(pi/3)-1/2 cos^2(pi/3)-7/8 ?
The value of sqrt(3)sin(pi/3)-1/2 cos^2(pi/3)-7/8 is 1/2