Solve left(sin(60)right)^2x-1=

$${ \left( \sin ( 60 ) \right) }^{ 2 } x-1=$$

Evaluate

$$\frac{3x}{4}-1$$

Solution Steps

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

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2^{2}}{2^{2}}.

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

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

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

The square of \sqrt{3} is 3.

$$\frac{3x}{2^{2}}-1$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3x}{4}-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4}{4}.

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

Since \frac{3x}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

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