Solve sin^2(30)+cos^2(45)

$$\sin ^ { 2 } ( 30 ) + \cos ^ { 2 } ( 45 )$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

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

$$\left(\frac{1}{2}\right)^{2}+\left(\cos(45)\right)^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

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

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

$$\frac{1}{4}+\left(\frac{\sqrt{2}}{2}\right)^{2}$$

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

$$\frac{1}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.

$$\frac{1}{4}+\frac{\left(\sqrt{2}\right)^{2}}{4}$$

Since \frac{1}{4} and \frac{\left(\sqrt{2}\right)^{2}}{4} have the same denominator, add them by adding their numerators.

$$\frac{1+\left(\sqrt{2}\right)^{2}}{4}$$

The square of \sqrt{2} is 2.

$$\frac{1}{4}+\frac{2}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{4}+\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}+\frac{1}{2}$$

Add \frac{1}{4} and \frac{1}{2} to get \frac{3}{4}.

$$\frac{3}{4}$$