Solve frac{cos^{2}45^circ}{tan30^circ*cos60^circ}+tan60^circ

$$\frac { \cos ^ { 2 } 45 ^ { \circ } } { \tan 30 ^ { \circ } \cdot \cos 60 ^ { \circ } } + \tan 60 ^ { \circ }$$

Evaluate

$$\sqrt{3}+\frac{2000000000000000}{1071796769724491}\approx 3.598076211$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{\cos^{2}(45)}{0.26794919243112275} + \tan(60)$$

Get the value of \cos(45) from trigonometric values table.

$$\frac{\left(\frac{\sqrt{2}}{2}\right)^{2}}{0.26794919243112275}+\tan(60)$$

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

$$\frac{\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}{0.26794919243112275}+\tan(60)$$

Express \frac{\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}{0.26794919243112275} as a single fraction.

$$\frac{\left(\sqrt{2}\right)^{2}}{2^{2}\times 0.26794919243112275}+\tan(60)$$

The square of \sqrt{2} is 2.

$$\frac{2}{2^{2}\times 0.26794919243112275}+\tan(60)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{4\times 0.26794919243112275}+\tan(60)$$

Multiply 4 and 0.26794919243112275 to get 1.071796769724491.

$$\frac{2}{1.071796769724491}+\tan(60)$$

Expand \frac{2}{1.071796769724491} by multiplying both numerator and the denominator by 1000000000000000.

$$\frac{2000000000000000}{1071796769724491}+\tan(60)$$

Get the value of \tan(60) from trigonometric values table.

$$\frac{2000000000000000}{1071796769724491}+\sqrt{3}$$