Solve 4sin(30)+2cos(45)-left(tan(60)right)^2

$$4 \sin ( 30 ) +2 \cos ( 45 ) - { \left( \tan ( 60 ) \right) }^{ 2 }$$

Evaluate

$$\sqrt{2}-1\approx 0.414213562$$

Solution Steps

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

$$4\times \frac{1}{2}+2\cos(45)-\left(\tan(60)\right)^{2}$$

Multiply 4 and \frac{1}{2} to get 2.

$$2+2\cos(45)-\left(\tan(60)\right)^{2}$$

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

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

Cancel out 2 and 2.

$$2+\sqrt{2}-\left(\tan(60)\right)^{2}$$

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

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

The square of \sqrt{3} is 3.

$$2+\sqrt{2}-3$$

Subtract 3 from 2 to get -1.

$$-1+\sqrt{2}$$