Solve 1/sinfrac{pi{4}}-cotpi/4

$$\frac { 1 } { \sin \frac { \pi } { 4 } } - \cot \frac { \pi } { 4 }$$

Evaluate

$$\sqrt{2}-1\approx 0.414213562$$

Solution Steps

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

$$\frac{1}{\frac{\sqrt{2}}{2}}-\cot(\frac{\pi }{4})$$

Divide 1 by \frac{\sqrt{2}}{2} by multiplying 1 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{2}{\sqrt{2}}-\cot(\frac{\pi }{4})$$

Rationalize the denominator of \frac{2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\cot(\frac{\pi }{4})$$

The square of \sqrt{2} is 2.

$$\frac{2\sqrt{2}}{2}-\cot(\frac{\pi }{4})$$

Cancel out 2 and 2.

$$\sqrt{2}-\cot(\frac{\pi }{4})$$

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

$$\sqrt{2}-1$$

Factor

$$\sqrt{2} - 1 = 0.414213562$$