What is the value of (pi/4 cos(pi/4)-sin(pi/4))/((pi/4)^2) ?

The value of (pi/4 cos(pi/4)-sin(pi/4))/((pi/4)^2) is (2sqrt(2)(pi-4))/(pi^2)

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(pi/4 cos(pi/4)-sin(pi/4))/((pi/4)^2)

\frac{\frac{π}{4} cos ( \frac{π}{4} ) - sin ( \frac{π}{4} )}{( \frac{π}{4} ) ^{2}}

\frac{2 2 ( π - 4 )}{π ^{2}}

Solution steps

\frac{\frac{π}{4} cos ( \frac{π}{4} ) - sin ( \frac{π}{4} )}{( \frac{π}{4} ) ^{2}}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

= \frac{\frac{π}{4} \cdot \frac{2}{2} - \frac{2}{2}}{( \frac{π}{4} ) ^{2}}

Simplify

\frac{\frac{π}{4} \cdot \frac{2}{2} - \frac{2}{2}}{( \frac{π}{4} ) ^{2}} : \frac{2 2 ( π - 4 )}{π ^{2}}

= \frac{2 2 ( π - 4 )}{π ^{2}}

cos^{2} (12 0^{\circ}) - sin^{2} (12 0^{\circ})

sin (arccos (\frac{2}{5}))

arcsin (0.91)

arcsin (0.72)

arcsin (0.46)

What is the value of (pi/4 cos(pi/4)-sin(pi/4))/((pi/4)^2) ?
The value of (pi/4 cos(pi/4)-sin(pi/4))/((pi/4)^2) is (2sqrt(2)(pi-4))/(pi^2)