Solve sin(30)+tan(30)sin(60))-tan(45)

$$\sin ( 30 ) + \tan ( 30) \sin ( 60 ) ) - \tan ( 45 )$$

Evaluate

$$1$$

Short Solution Steps

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

$$\frac{1}{2}+\tan(30)\sin(60)$$

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

$$\frac{1}{2}+\frac{\sqrt{3}}{3}\sin(60)$$

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

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

Multiply \frac{\sqrt{3}}{3} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3\times 2 is 2\times 3. Multiply \frac{1}{2} times \frac{3}{3}.

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

Since \frac{3}{2\times 3} and \frac{\sqrt{3}\sqrt{3}}{2\times 3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3+\sqrt{3}\sqrt{3}.

$$\frac{3+3}{2\times 3}$$

Do the calculations in 3+3.

$$\frac{6}{2\times 3}$$

Expand 2\times 3.

$$\frac{6}{6}$$

Divide 6 by 6 to get 1.

$$1$$