Solve {l}{sin^245}{+tan^24}

$$\left. \begin{array} { l } { \sin ^ { 2 } 45 } \\ { + \tan ^ { 2 } 4 } \end{array} \right.$$

Evaluate

$$0.5048897590285830701234169137783681$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\sin^{2}(45) + 0.06992681194351041 ^ {2}$$

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

$$\left(\frac{\sqrt{2}}{2}\right)^{2}+0.06992681194351041^{2}$$

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

$$\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+0.06992681194351041^{2}$$

Calculate 0.06992681194351041 to the power of 2 and get 0.0048897590285830701234169137783681.

$$\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+0.0048897590285830701234169137783681$$

The square of \sqrt{2} is 2.

$$\frac{2}{2^{2}}+0.0048897590285830701234169137783681$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{4}+0.0048897590285830701234169137783681$$

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

$$\frac{1}{2}+0.0048897590285830701234169137783681$$

Add \frac{1}{2} and 0.0048897590285830701234169137783681 to get \frac{5048897590285830701234169137783681}{10000000000000000000000000000000000}.

$$\frac{5048897590285830701234169137783681}{10000000000000000000000000000000000}$$