Solve sin^{2}45^{circ}-cos60^circ+tan60^circ*cos^230^circ

$$\sin ^ { 2 } 45 ^ { \circ } - \cos 60 ^ { \circ } + \tan 60 ^ { \circ } \times \cos ^ { 2 } 30 ^ { \circ }$$

Evaluate

$$1.0000000000000004$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\sin^{2}(45) - \cos(60) + 1.0000000000000004$$

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

$$\left(\frac{\sqrt{2}}{2}\right)^{2}-\cos(60)+1.0000000000000004$$

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

$$\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}-\cos(60)+1.0000000000000004$$

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

$$\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}-\frac{1}{2}+1.0000000000000004$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2^{2} and 2 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

$$\frac{\left(\sqrt{2}\right)^{2}}{4}-\frac{2}{4}+1.0000000000000004$$

Since \frac{\left(\sqrt{2}\right)^{2}}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\sqrt{2}\right)^{2}-2}{4}+1.0000000000000004$$

The square of \sqrt{2} is 2.

$$\frac{2-2}{4}+1.0000000000000004$$

Subtract 2 from 2 to get 0.

$$\frac{0}{4}+1.0000000000000004$$

Zero divided by any non-zero number gives zero.

$$0+1.0000000000000004$$

Add 0 and 1.0000000000000004 to get 1.0000000000000004.

$$1.0000000000000004$$