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

The value of cos(60)cos(45)+sin(60)sin(45) is (sqrt(2)(1+sqrt(3)))/4

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cos(60)cos(45)+sin(60)sin(45)

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

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

Solution steps

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

sin (6 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}

sin (12 0^{\circ}) cos (6 0^{\circ}) - cos (12 0^{\circ}) sin (6 0^{\circ})

2 arctan (0)

sin (2 \cdot 30)

arctan (\frac{- 1}{- 1})

- sin (3)

What is the value of cos(60)cos(45)+sin(60)sin(45) ?
The value of cos(60)cos(45)+sin(60)sin(45) is (sqrt(2)(1+sqrt(3)))/4