What is the value of cos(45)cos(60)-sin(45)sin(60) ?

The value of cos(45)cos(60)-sin(45)sin(60) is (sqrt(2)-sqrt(6))/4

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cos(45)cos(60)-sin(45)sin(60)

cos (4 5^{\circ}) cos (6 0^{\circ}) - sin (4 5^{\circ}) sin (6 0^{\circ})

\frac{2 - 6}{4}

Solution steps

cos (4 5^{\circ}) cos (6 0^{\circ}) - sin (4 5^{\circ}) sin (6 0^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (6 0^{\circ}) = \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}

2 cos (5 π)

arcsin (sin (\frac{11 π}{5}))

\frac{0}{sin ( 0 )}

sin^{4} (3 0^{\circ})

0 + sin (0)

What is the value of cos(45)cos(60)-sin(45)sin(60) ?
The value of cos(45)cos(60)-sin(45)sin(60) is (sqrt(2)-sqrt(6))/4