Solve sin^2(pi/4)+cos^2(pi/4)=

$$\sin ^ { 2 } ( \frac { \pi } { 4 } ) + \cos ^ { 2 } ( \frac { \pi } { 4 } ) =$$

Evaluate

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Solution Steps

Get the value of \sin(\frac{\pi }{4}) from trigonometric values table.

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

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

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

Get the value of \cos(\frac{\pi }{4}) from trigonometric values table.

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

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

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

Combine \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} and \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} to get 2\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}.

$$2\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}$$

The square of \sqrt{2} is 2.

$$2\times \frac{2}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$2\times \frac{2}{4}$$

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

$$2\times \frac{1}{2}$$

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

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Factor

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