Solve sin(45^circ)*cos(30^circ)+cos(30^circ)*sin(45^circ)

$$\sin ( 45 ^ { \circ } ) \times \cos ( 30 ^ { \circ } ) + \cos ( 30 ^ { \circ } ) \times \sin ( 45 ^ { \circ } )$$

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

Get the value of \sin(45) from trigonometric values table.

$$\frac{\sqrt{2}}{2}\cos(30)+\cos(30)\sin(45)$$

Get the value of \cos(30) from trigonometric values table.

$$\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}+\cos(30)\sin(45)$$

Multiply \frac{\sqrt{2}}{2} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{2}\sqrt{3}}{2\times 2}+\cos(30)\sin(45)$$

Get the value of \cos(30) from trigonometric values table.

$$\frac{\sqrt{2}\sqrt{3}}{2\times 2}+\frac{\sqrt{3}}{2}\sin(45)$$

Get the value of \sin(45) from trigonometric values table.

$$\frac{\sqrt{2}\sqrt{3}}{2\times 2}+\frac{\sqrt{3}}{2}\times \frac{\sqrt{2}}{2}$$

Multiply \frac{\sqrt{3}}{2} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{2}\sqrt{3}}{2\times 2}+\frac{\sqrt{3}\sqrt{2}}{2\times 2}$$

Combine \frac{\sqrt{2}\sqrt{3}}{2\times 2} and \frac{\sqrt{3}\sqrt{2}}{2\times 2} to get 2\times \frac{\sqrt{2}\sqrt{3}}{2\times 2}.

$$2\times \frac{\sqrt{2}\sqrt{3}}{2\times 2}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$2\times \frac{\sqrt{6}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$2\times \frac{\sqrt{6}}{4}$$

Cancel out 4, the greatest common factor in 2 and 4.

$$\frac{\sqrt{6}}{2}$$