Solve 6sin(60-45)/cos(45)

$$\frac{ 6 \sin ( 60-45 ) }{ \cos ( 45 ) }$$

Evaluate

$$\frac{38822856765378111\sqrt{2}}{25000000000000000}\approx 2.196152423$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{6 \cdot 0.25881904510252074}{\cos(45)}$$

Multiply 6 and 0.25881904510252074 to get 1.55291427061512444.

$$\frac{1.55291427061512444}{\cos(45)}$$

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

$$\frac{1.55291427061512444}{\frac{\sqrt{2}}{2}}$$

Divide 1.55291427061512444 by \frac{\sqrt{2}}{2} by multiplying 1.55291427061512444 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{1.55291427061512444\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{1.55291427061512444\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{1.55291427061512444\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{1.55291427061512444\times 2\sqrt{2}}{2}$$

Multiply 1.55291427061512444 and 2 to get 3.10582854123024888.

$$\frac{3.10582854123024888\sqrt{2}}{2}$$

Divide 3.10582854123024888\sqrt{2} by 2 to get 1.55291427061512444\sqrt{2}.

$$1.55291427061512444\sqrt{2}$$