What is the value of cos(pi/3)-sin((3pi)/4) ?

The value of cos(pi/3)-sin((3pi)/4) is (1-sqrt(2))/2

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cos(pi/3)-sin((3pi)/4)

cos (\frac{π}{3}) - sin (\frac{3 π}{4})

\frac{1 - 2}{2}

Solution steps

cos (\frac{π}{3}) - sin (\frac{3 π}{4})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

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

Simplify

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

= \frac{1 - 2}{2}

arctan (\frac{16}{8})

sin (7 0^{\circ}) 10

sin (\frac{3 π}{4}) cos (\frac{π}{12}) + cos (\frac{3 π}{4}) sin (\frac{π}{12})

arccos (0.5)

3 tan (9 0^{\circ})

What is the value of cos(pi/3)-sin((3pi)/4) ?
The value of cos(pi/3)-sin((3pi)/4) is (1-sqrt(2))/2