Solve tan48^circ/cos45^circ

$$\frac { \tan 48 ^ { \circ } } { \cos 45 ^ { \circ } }$$

Evaluate

$$\frac{1388265643536491\sqrt{2}}{1250000000000000}\approx 1.570643281$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1.1106125148291928}{\cos(45)}$$

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

$$\frac{1.1106125148291928}{\frac{\sqrt{2}}{2}}$$

Divide 1.1106125148291928 by \frac{\sqrt{2}}{2} by multiplying 1.1106125148291928 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{1.1106125148291928\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{1.1106125148291928\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{1.1106125148291928\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{1.1106125148291928\times 2\sqrt{2}}{2}$$

Multiply 1.1106125148291928 and 2 to get 2.2212250296583856.

$$\frac{2.2212250296583856\sqrt{2}}{2}$$

Divide 2.2212250296583856\sqrt{2} by 2 to get 1.1106125148291928\sqrt{2}.

$$1.1106125148291928\sqrt{2}$$