Solve ffrac{sin60^{circ}+cot45^{circ}-csc30^circ}{sec60^circ-cos30^circ+tan45^circ}

$$f \frac { \sin 60 ^ { \circ } + \cot 45 ^ { \circ } - \csc 30 ^ { \circ } } { \sec 60 ^ { \circ } - \cos 30 ^ { \circ } + \tan 45 ^ { \circ } }$$

Evaluate

$$\frac{4\sqrt{3}f}{33}-\frac{3f}{11}$$

Solution Steps

Get the value of \sin(60) from trigonometric values table.

$$f\times \frac{\frac{\sqrt{3}}{2}+\cot(45)-\csc(30)}{\sec(60)-\cos(30)+\tan(45)}$$

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

$$f\times \frac{\frac{\sqrt{3}}{2}+1-\csc(30)}{\sec(60)-\cos(30)+\tan(45)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$f\times \frac{\frac{\sqrt{3}}{2}+\frac{2}{2}-\csc(30)}{\sec(60)-\cos(30)+\tan(45)}$$

Since \frac{\sqrt{3}}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$f\times \frac{\frac{\sqrt{3}+2}{2}-\csc(30)}{\sec(60)-\cos(30)+\tan(45)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \csc(30) times \frac{2}{2}.

$$f\times \frac{\frac{\sqrt{3}+2}{2}-\frac{2\csc(30)}{2}}{\sec(60)-\cos(30)+\tan(45)}$$

Since \frac{\sqrt{3}+2}{2} and \frac{2\csc(30)}{2} have the same denominator, subtract them by subtracting their numerators.

$$f\times \frac{\frac{\sqrt{3}+2-2\csc(30)}{2}}{\sec(60)-\cos(30)+\tan(45)}$$

Get the value of \cos(30) from trigonometric values table.

$$f\times \frac{\frac{\sqrt{3}+2-2\csc(30)}{2}}{\sec(60)-\frac{\sqrt{3}}{2}+\tan(45)}$$

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

$$f\times \frac{\frac{\sqrt{3}+2-2\csc(30)}{2}}{\sec(60)-\frac{\sqrt{3}}{2}+1}$$

Express \frac{\frac{\sqrt{3}+2-2\csc(30)}{2}}{\sec(60)-\frac{\sqrt{3}}{2}+1} as a single fraction.

$$f\times \frac{\sqrt{3}+2-2\csc(30)}{2\left(\sec(60)-\frac{\sqrt{3}}{2}+1\right)}$$

Use the distributive property to multiply 2 by \sec(60)-\frac{\sqrt{3}}{2}+1.

$$f\times \frac{\sqrt{3}+2-2\csc(30)}{2\sec(60)-2\times \frac{\sqrt{3}}{2}+2}$$

Cancel out 2 and 2.

$$f\times \frac{\sqrt{3}+2-2\csc(30)}{2\sec(60)-\sqrt{3}+2}$$

Express f\times \frac{\sqrt{3}+2-2\csc(30)}{2\sec(60)-\sqrt{3}+2} as a single fraction.

$$\frac{f\left(\sqrt{3}+2-2\csc(30)\right)}{2\sec(60)-\sqrt{3}+2}$$

Use the distributive property to multiply f by \sqrt{3}+2-2\csc(30).

$$\frac{f\sqrt{3}+2f-2f\csc(30)}{2\sec(60)-\sqrt{3}+2}$$