Solve -3tan^245^circ/cos^230^circ

$$\frac { - 3 \tan ^ { 2 } 45 ^ { \circ } } { \cos ^ { 2 } 30 ^ { \circ } }$$

Evaluate

$$-4$$

Solution Steps

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

$$\frac{-3\times 1^{2}}{\left(\cos(30)\right)^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{-3}{\left(\cos(30)\right)^{2}}$$

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

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

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

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

Divide -3 by \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} by multiplying -3 by the reciprocal of \frac{\left(\sqrt{3}\right)^{2}}{2^{2}}.

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

Calculate 2 to the power of 2 and get 4.

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

Multiply -3 and 4 to get -12.

$$\frac{-12}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{-12}{3}$$

Divide -12 by 3 to get -4.

$$-4$$