Solve 8left(cos(30)right)^2-4

$$8 { \left( \cos ( 30 ) \right) }^{ 2 } -4$$

Evaluate

$$2$$

Solution Steps

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

$$8\times \left(\frac{\sqrt{3}}{2}\right)^{2}-4$$

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

$$8\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-4$$

Express 8\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} as a single fraction.

$$\frac{8\left(\sqrt{3}\right)^{2}}{2^{2}}-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2^{2}}{2^{2}}.

$$\frac{8\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{4\times 2^{2}}{2^{2}}$$

Since \frac{8\left(\sqrt{3}\right)^{2}}{2^{2}} and \frac{4\times 2^{2}}{2^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8\left(\sqrt{3}\right)^{2}-4\times 2^{2}}{2^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{8\times 3}{2^{2}}-4$$

Multiply 8 and 3 to get 24.

$$\frac{24}{2^{2}}-4$$

Calculate 2 to the power of 2 and get 4.

$$\frac{24}{4}-4$$

Divide 24 by 4 to get 6.

$$6-4$$

Subtract 4 from 6 to get 2.

$$2$$