What is the value of sin(30)cos(45)-cos(30)sin(45) ?

The value of sin(30)cos(45)-cos(30)sin(45) is (sqrt(2)(1-sqrt(3)))/4

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sin(30)cos(45)-cos(30)sin(45)

sin (3 0^{\circ}) cos (4 5^{\circ}) - cos (3 0^{\circ}) sin (4 5^{\circ})

\frac{2 ( 1 - 3 )}{4}

Solution steps

sin (3 0^{\circ}) cos (4 5^{\circ}) - cos (3 0^{\circ}) sin (4 5^{\circ})

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

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

Simplify

\frac{1}{2} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2} : \frac{2 ( 1 - 3 )}{4}

= \frac{2 ( 1 - 3 )}{4}

\frac{15}{sin ( 4 5 ^{\circ} )}

cos (arcsin (\frac{12}{13}) + arctan (\frac{3}{4}))

arctan (0.833)

0.6 cos (3 0^{\circ})

ln cos (\frac{π}{4})

What is the value of sin(30)cos(45)-cos(30)sin(45) ?
The value of sin(30)cos(45)-cos(30)sin(45) is (sqrt(2)(1-sqrt(3)))/4