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

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

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

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

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

Solution steps

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

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

Simplify

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

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

2 sin (1 7^{\circ}) cos (1 7^{\circ})

arccos (0.19)

arccos (0.22)

arccos (0.31)

arccos (0.43)

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