What is the value of (pi/6 cos(pi/6)-sin(pi/6))/((pi/6)^2) ?

The value of (pi/6 cos(pi/6)-sin(pi/6))/((pi/6)^2) is (3(sqrt(3)pi-6))/(pi^2)

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(pi/6 cos(pi/6)-sin(pi/6))/((pi/6)^2)

\frac{\frac{π}{6} cos ( \frac{π}{6} ) - sin ( \frac{π}{6} )}{( \frac{π}{6} ) ^{2}}

\frac{3 ( 3 π - 6 )}{π ^{2}}

Solution steps

\frac{\frac{π}{6} cos ( \frac{π}{6} ) - sin ( \frac{π}{6} )}{( \frac{π}{6} ) ^{2}}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

= \frac{\frac{π}{6} \cdot \frac{3}{2} - \frac{1}{2}}{( \frac{π}{6} ) ^{2}}

Simplify

\frac{\frac{π}{6} \cdot \frac{3}{2} - \frac{1}{2}}{( \frac{π}{6} ) ^{2}} : \frac{3 ( 3 π - 6 )}{π ^{2}}

= \frac{3 ( 3 π - 6 )}{π ^{2}}

2 cos (\frac{π}{2}) + sin (π)

6 cos (\frac{11 π}{6})

\frac{1}{sin ( \frac{π}{3} )}

cos (34 0^{\circ})

sin (25 5^{\circ}) - sin (19 5^{\circ})

What is the value of (pi/6 cos(pi/6)-sin(pi/6))/((pi/6)^2) ?
The value of (pi/6 cos(pi/6)-sin(pi/6))/((pi/6)^2) is (3(sqrt(3)pi-6))/(pi^2)