Solve k:sin^{2}30^{circ}+cos^260^circ+tan60^circcos30^circ=

$$k : \sin ^ { 2 } 30 ^ { \circ } + \cos ^ { 2 } 60 ^ { \circ } + \tan 60 ^ { \circ } \cos 30 ^ { \circ } =$$

Evaluate

$$4k+\frac{7}{4}$$

Short Solution Steps

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

$$\frac{k}{\left(\frac{1}{2}\right)^{2}}+\left(\cos(60)\right)^{2}+\tan(60)\cos(30)$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{k}{\frac{1}{4}}+\left(\cos(60)\right)^{2}+\tan(60)\cos(30)$$

Divide k by \frac{1}{4} by multiplying k by the reciprocal of \frac{1}{4}.

$$k\times 4+\left(\cos(60)\right)^{2}+\tan(60)\cos(30)$$

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

$$k\times 4+\left(\frac{1}{2}\right)^{2}+\tan(60)\cos(30)$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$k\times 4+\frac{1}{4}+\tan(60)\cos(30)$$

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

$$k\times 4+\frac{1}{4}+\sqrt{3}\cos(30)$$

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

$$k\times 4+\frac{1}{4}+\sqrt{3}\times \frac{\sqrt{3}}{2}$$

Express \sqrt{3}\times \frac{\sqrt{3}}{2} as a single fraction.

$$k\times 4+\frac{1}{4}+\frac{\sqrt{3}\sqrt{3}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{\sqrt{3}\sqrt{3}}{2} times \frac{2}{2}.

$$k\times 4+\frac{1}{4}+\frac{2\sqrt{3}\sqrt{3}}{4}$$

Since \frac{1}{4} and \frac{2\sqrt{3}\sqrt{3}}{4} have the same denominator, add them by adding their numerators.

$$k\times 4+\frac{1+2\sqrt{3}\sqrt{3}}{4}$$

Do the multiplications in 1+2\sqrt{3}\sqrt{3}.

$$k\times 4+\frac{1+6}{4}$$

Do the calculations in 1+6.

$$k\times 4+\frac{7}{4}$$