Solve cos(30)-sin(30)*sin(30)/cos(30)

$$\cos ( 30 ) - \frac{ \sin ( 30 ) \times \sin ( 30 ) }{ \cos ( 30 ) }$$

Evaluate

$$\frac{\sqrt{3}}{3}\approx 0.577350269$$

Solution Steps

Multiply \sin(30) and \sin(30) to get \left(\sin(30)\right)^{2}.

$$\cos(30)-\frac{\left(\sin(30)\right)^{2}}{\cos(30)}$$

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

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

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

$$\frac{\sqrt{3}}{2}-\frac{\left(\frac{1}{2}\right)^{2}}{\cos(30)}$$

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

$$\frac{\sqrt{3}}{2}-\frac{\frac{1}{4}}{\cos(30)}$$

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

$$\frac{\sqrt{3}}{2}-\frac{\frac{1}{4}}{\frac{\sqrt{3}}{2}}$$

Divide \frac{1}{4} by \frac{\sqrt{3}}{2} by multiplying \frac{1}{4} by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{\sqrt{3}}{2}-\frac{2}{4\sqrt{3}}$$

Rationalize the denominator of \frac{2}{4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{2}-\frac{2\sqrt{3}}{4\times 3}$$

Cancel out 2 in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{6}$$

Combine \frac{\sqrt{3}}{2} and -\frac{\sqrt{3}}{6} to get \frac{1}{3}\sqrt{3}.

$$\frac{1}{3}\sqrt{3}$$