Solve 2{left(cos(30^circ)right)}^2+3{left(sin(30^circ)right)}^2=

$$2 { \left( \cos ( 30 ^ { \circ } ) \right) }^{ 2 } +3 { \left( \sin ( 30 ^ { \circ } ) \right) }^{ 2 } =$$

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

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

$$2\times \left(\frac{\sqrt{3}}{2}\right)^{2}+3\left(\sin(30)\right)^{2}$$

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$2\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+3\left(\sin(30)\right)^{2}$$

Express 2\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} as a single fraction.

$$\frac{2\left(\sqrt{3}\right)^{2}}{2^{2}}+3\left(\sin(30)\right)^{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\left(\sqrt{3}\right)^{2}}{2}+3\left(\sin(30)\right)^{2}$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{2}+3\times \left(\frac{1}{2}\right)^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{\left(\sqrt{3}\right)^{2}}{2}+3\times \frac{1}{4}$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{\left(\sqrt{3}\right)^{2}}{2}+\frac{3}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{\left(\sqrt{3}\right)^{2}}{2} times \frac{2}{2}.

$$\frac{2\left(\sqrt{3}\right)^{2}}{4}+\frac{3}{4}$$

Since \frac{2\left(\sqrt{3}\right)^{2}}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{2\left(\sqrt{3}\right)^{2}+3}{4}$$

The square of \sqrt{3} is 3.

$$\frac{3}{2}+\frac{3}{4}$$

Add \frac{3}{2} and \frac{3}{4} to get \frac{9}{4}.

$$\frac{9}{4}$$