Solve frac{tan^{2}45^{circ}-sin^230^circ}{tan60^circ*cos30^circ}

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

Evaluate

$$\frac{3750000000000000}{6390857459152187}\approx 0.586775722$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{\tan^{2}(45) - \sin^{2}(30)}{1.2781714918304374}$$

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

$$\frac{1^{2}-\left(\sin(30)\right)^{2}}{1.2781714918304374}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1-\left(\sin(30)\right)^{2}}{1.2781714918304374}$$

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

$$\frac{1-\left(\frac{1}{2}\right)^{2}}{1.2781714918304374}$$

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

$$\frac{1-\frac{1}{4}}{1.2781714918304374}$$

Subtract \frac{1}{4} from 1 to get \frac{3}{4}.

$$\frac{\frac{3}{4}}{1.2781714918304374}$$

Express \frac{\frac{3}{4}}{1.2781714918304374} as a single fraction.

$$\frac{3}{4\times 1.2781714918304374}$$

Multiply 4 and 1.2781714918304374 to get 5.1126859673217496.

$$\frac{3}{5.1126859673217496}$$

Expand \frac{3}{5.1126859673217496} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{30000000000000000}{51126859673217496}$$

Reduce the fraction \frac{30000000000000000}{51126859673217496} to lowest terms by extracting and canceling out 8.

$$\frac{3750000000000000}{6390857459152187}$$