What is the value of sin(pi/4)cos(pi/6)-cos(pi/4)sin(pi/6) ?

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

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sin(pi/4)cos(pi/6)-cos(pi/4)sin(pi/6)

sin (\frac{π}{4}) cos (\frac{π}{6}) - cos (\frac{π}{4}) sin (\frac{π}{6})

\frac{6 - 2}{4}

Solution steps

sin (\frac{π}{4}) cos (\frac{π}{6}) - cos (\frac{π}{4}) sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

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

Simplify

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

= \frac{6 - 2}{4}

\frac{tan ( 5 ^{\circ} ) + tan ( 4 0 ^{\circ} )}{1 - tan ( 5 ^{\circ} ) tan ( 4 0 ^{\circ} )}

arctan (\frac{7}{0})

cos (\frac{16 π}{9})

57 sin (2 9^{\circ})

arctan (\frac{4.9}{2.9})

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