Solve tan^{2}45^circ4cos^230^circ-sin^260

$$\tan ^ { 2 } 45 ^ { \circ } 4 \cos ^ { 2 } 30 ^ { \circ } - \sin ^ { 2 } 60$$

Evaluate

$$-\frac{3}{4}=-0.75$$

Solution Steps

Multiply 45 and 4 to get 180.

$$\left(\tan(180)\right)^{2}\left(\cos(30)\right)^{2}-\left(\sin(60)\right)^{2}$$

Get the value of \tan(180) from trigonometric values table.

$$0^{2}\left(\cos(30)\right)^{2}-\left(\sin(60)\right)^{2}$$

Calculate 0 to the power of 2 and get 0.

$$0\left(\cos(30)\right)^{2}-\left(\sin(60)\right)^{2}$$

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

$$0\times \left(\frac{\sqrt{3}}{2}\right)^{2}-\left(\sin(60)\right)^{2}$$

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

$$0\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\left(\sin(60)\right)^{2}$$

Express 0\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} as a single fraction.

$$\frac{0\left(\sqrt{3}\right)^{2}}{2^{2}}-\left(\sin(60)\right)^{2}$$

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

$$\frac{0\left(\sqrt{3}\right)^{2}}{2^{2}}-\left(\frac{\sqrt{3}}{2}\right)^{2}$$

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

$$\frac{0\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{0\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{3}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{0\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{3}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.

$$\frac{0\left(\sqrt{3}\right)^{2}}{4}-\frac{3}{4}$$

Since \frac{0\left(\sqrt{3}\right)^{2}}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{0\left(\sqrt{3}\right)^{2}-3}{4}$$

The square of \sqrt{3} is 3.

$$\frac{0\times 3}{2^{2}}-\frac{3}{4}$$

Multiply 0 and 3 to get 0.

$$\frac{0}{2^{2}}-\frac{3}{4}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{0}{4}-\frac{3}{4}$$

Zero divided by any non-zero number gives zero.

$$0-\frac{3}{4}$$

Subtract \frac{3}{4} from 0 to get -\frac{3}{4}.

$$-\frac{3}{4}$$