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

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

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cos(45)sin(30)+sin(45)cos(30)

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

\frac{2 + 6}{4}

Solution steps

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

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}

Use the following trivial identity:

cos (3 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}

tanh (3)

12 cos (5 0^{\circ})

arccos (\frac{2}{2})

6 cos (8 0^{\circ})

arccot (- 5)

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