Solve (sqrt{3}cospi/6+sinpi/6)operatornamectg^2pi/4

$$( \sqrt { 3 } \cos \frac { \pi } { 6 } + \sin \frac { \pi } { 6 } ) \operatorname { ctg } ^ { 2 } \frac { \pi } { 4 }$$

Evaluate

$$2$$

Short Solution Steps

Get the value of \cos(\frac{\pi }{6}) from trigonometric values table.

$$\left(\sqrt{3}\times \frac{\sqrt{3}}{2}+\sin(\frac{\pi }{6})\right)\left(\cot(\frac{\pi }{4})\right)^{2}$$

Express \sqrt{3}\times \frac{\sqrt{3}}{2} as a single fraction.

$$\left(\frac{\sqrt{3}\sqrt{3}}{2}+\sin(\frac{\pi }{6})\right)\left(\cot(\frac{\pi }{4})\right)^{2}$$

Get the value of \sin(\frac{\pi }{6}) from trigonometric values table.

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

Since \frac{\sqrt{3}\sqrt{3}}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \sqrt{3}\sqrt{3}+1.

$$\frac{3+1}{2}\left(\cot(\frac{\pi }{4})\right)^{2}$$

Do the calculations in 3+1.

$$\frac{4}{2}\left(\cot(\frac{\pi }{4})\right)^{2}$$

Get the value of \cot(\frac{\pi }{4}) from trigonometric values table.

$$\frac{4}{2}\times 1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{4}{2}\times 1$$

Express \frac{4}{2}\times 1 as a single fraction.

$$\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$2$$

Factor

$$2$$