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})

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{5 π}{12}) - sin (\frac{π}{12})

cos (8 7^{\circ})

cos (2 \frac{π}{3})

4 - 2 arctan (4)

sec (\frac{11 π}{4})

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