Solve (2-sqrt{3})*tan60^circ+tan45^circ/1-tan60^circtan45^circ

$$( 2 - \sqrt { 3 } ) \cdot \frac { \tan 60 ^ { \circ } + \tan 45 ^ { \circ } } { 1 - \tan 60 ^ { \circ } \tan 45 ^ { \circ } }$$

Evaluate

$$-1$$

Solution Steps

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

$$\left(2-\sqrt{3}\right)\times \frac{\sqrt{3}+\tan(45)}{1-\tan(60)\tan(45)}$$

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

$$\left(2-\sqrt{3}\right)\times \frac{\sqrt{3}+1}{1-\tan(60)\tan(45)}$$

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

$$\left(2-\sqrt{3}\right)\times \frac{\sqrt{3}+1}{1-\sqrt{3}\tan(45)}$$

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

$$\left(2-\sqrt{3}\right)\times \frac{\sqrt{3}+1}{1-\sqrt{3}\times 1}$$

Express \left(2-\sqrt{3}\right)\times \frac{\sqrt{3}+1}{1-\sqrt{3}\times 1} as a single fraction.

$$\frac{\left(2-\sqrt{3}\right)\left(\sqrt{3}+1\right)}{1-\sqrt{3}\times 1}$$

Use the distributive property to multiply 2-\sqrt{3} by \sqrt{3}+1 and combine like terms.

$$\frac{\sqrt{3}+2-\left(\sqrt{3}\right)^{2}}{1-\sqrt{3}\times 1}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}+2-3}{1-\sqrt{3}\times 1}$$

Subtract 3 from 2 to get -1.

$$\frac{\sqrt{3}-1}{1-\sqrt{3}\times 1}$$

Extract the negative sign in \sqrt{3}-1.

$$\frac{-\left(-\sqrt{3}+1\right)}{-\sqrt{3}+1}$$

Cancel out -\sqrt{3}+1 in both numerator and denominator.

$$-1$$