Solve sin^2(pi/3)/cot(frac{pi{3})sin(pi/3)}

$$\frac { \sin ^ { 2 } ( \frac { \pi } { 3 } ) } { \cot ( \frac { \pi } { 3 } ) \sin ( \frac { \pi } { 3 } ) }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Get the value of \sin(\frac{\pi }{3}) from trigonometric values table.

$$\frac{\left(\frac{\sqrt{3}}{2}\right)^{2}}{\cot(\frac{\pi }{3})\sin(\frac{\pi }{3})}$$

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

$$\frac{\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}}{\cot(\frac{\pi }{3})\sin(\frac{\pi }{3})}$$

Get the value of \cot(\frac{\pi }{3}) from trigonometric values table.

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

Get the value of \sin(\frac{\pi }{3}) from trigonometric values table.

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

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

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

Divide \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} by \frac{\sqrt{3}\sqrt{3}}{3\times 2} by multiplying \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} by the reciprocal of \frac{\sqrt{3}\sqrt{3}}{3\times 2}.

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

Cancel out 2\sqrt{3}\sqrt{3} in both numerator and denominator.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$