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

The value of (cos(45))(cos(30))-(sin(45))(sin(30)) is (sqrt(6)-sqrt(2))/4

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

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

\frac{6 - 2}{4}

Solution steps

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

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

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}

Use the following trivial identity:

sin (3 0^{\circ}) = \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}

sin (\frac{173}{210})

60 (4)^{4} - 12 cos (4)

\frac{20}{sin ( 3 2 ^{\circ} )}

2 csc (2)

4 (cos (6 0^{\circ}) + i sin (6 0^{\circ}))

What is the value of (cos(45))(cos(30))-(sin(45))(sin(30)) ?
The value of (cos(45))(cos(30))-(sin(45))(sin(30)) is (sqrt(6)-sqrt(2))/4