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

The value of sin(pi/4)cos(pi/3)-cos(pi/4)sin(pi/3) is (sqrt(2)-sqrt(6))/4

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

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

\frac{2 - 6}{4}

Solution steps

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

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

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

Simplify

\frac{2}{2} \cdot \frac{1}{2} - \frac{2}{2} \cdot \frac{3}{2} : \frac{2 - 6}{4}

= \frac{2 - 6}{4}

4983 \cdot cos (4 0^{\circ})

\frac{sin ( tan ( 12.4 \cdot 0 ) )}{6.2 \cdot 0}

arcsin (0.5) - e^{- 2 (0.5)}

\frac{( 2.68 \cdot 9.80665 )}{sin ( 7 5 ^{\circ} )}

\frac{22.4}{sin ( 7 1 ^{\circ} )}

What is the value of sin(pi/4)cos(pi/3)-cos(pi/4)sin(pi/3) ?
The value of sin(pi/4)cos(pi/3)-cos(pi/4)sin(pi/3) is (sqrt(2)-sqrt(6))/4