Solve frac{5cos(0)-2sin(30)+sqrt{3}cos(30)}{tan(30)*tan(60)*cos(60)}+3sin(29)sec(61)

$$\frac{ 5 \cos ( 0 ) -2 \sin ( 30 ) + \sqrt{ 3 } \cos ( 30 ) }{ \tan ( 30 ) \times \tan ( 60 ) \times \cos ( 60 ) } +3 \sin ( 29 ) \sec ( 61 )$$

Evaluate

$$13.99999999999999987246512207937052$$

Short Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{5 \cos(0) - 2 \sin(30) + \sqrt{3} \cos(30)}{\tan(30) \cdot \tan(60) \cdot \cos(60)} + 3 \cdot 0.48480962024633706 \cdot 2.062665339627314$$

Get the value of \cos(0) from trigonometric values table.

$$\frac{5\times 1-2\sin(30)+\sqrt{3}\cos(30)}{\tan(30)\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

Multiply 5 and 1 to get 5.

$$\frac{5-2\sin(30)+\sqrt{3}\cos(30)}{\tan(30)\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{5-2\times \frac{1}{2}+\sqrt{3}\cos(30)}{\tan(30)\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

Multiply 2 and \frac{1}{2} to get 1.

$$\frac{5-1+\sqrt{3}\cos(30)}{\tan(30)\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

Subtract 1 from 5 to get 4.

$$\frac{4+\sqrt{3}\cos(30)}{\tan(30)\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{4+\sqrt{3}\times \frac{\sqrt{3}}{2}}{\tan(30)\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{4+\frac{\sqrt{3}\sqrt{3}}{2}}{\tan(30)\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

$$\frac{\frac{4\times 2}{2}+\frac{\sqrt{3}\sqrt{3}}{2}}{\tan(30)\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{\frac{4\times 2+\sqrt{3}\sqrt{3}}{2}}{\tan(30)\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

Do the multiplications in 4\times 2+\sqrt{3}\sqrt{3}.

$$\frac{\frac{8+3}{2}}{\tan(30)\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

Do the calculations in 8+3.

$$\frac{\frac{11}{2}}{\tan(30)\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{\frac{11}{2}}{\frac{\sqrt{3}}{3}\tan(60)\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{\frac{11}{2}}{\frac{\sqrt{3}}{3}\sqrt{3}\cos(60)}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{\frac{11}{2}}{\frac{\sqrt{3}}{3}\sqrt{3}\times \frac{1}{2}}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{\frac{11}{2}}{\frac{\sqrt{3}\sqrt{3}}{3}\times \frac{1}{2}}+3\times 0.48480962024633706\times 2.062665339627314$$

Multiply \frac{\sqrt{3}\sqrt{3}}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{11}{2}}{\frac{\sqrt{3}\sqrt{3}}{3\times 2}}+3\times 0.48480962024633706\times 2.062665339627314$$

Divide \frac{11}{2} by \frac{\sqrt{3}\sqrt{3}}{3\times 2} by multiplying \frac{11}{2} by the reciprocal of \frac{\sqrt{3}\sqrt{3}}{3\times 2}.

$$\frac{11\times 3\times 2}{2\sqrt{3}\sqrt{3}}+3\times 0.48480962024633706\times 2.062665339627314$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\times 11}{\sqrt{3}\sqrt{3}}+3\times 0.48480962024633706\times 2.062665339627314$$

Rationalize the denominator of \frac{3\times 11}{\sqrt{3}\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{3\times 11\sqrt{3}}{\left(\sqrt{3}\right)^{2}\sqrt{3}}+3\times 0.48480962024633706\times 2.062665339627314$$

The square of \sqrt{3} is 3.

$$\frac{3\times 11\sqrt{3}}{3\sqrt{3}}+3\times 0.48480962024633706\times 2.062665339627314$$

Cancel out \sqrt{3} in both numerator and denominator.

$$\frac{3\times 11}{3}+3\times 0.48480962024633706\times 2.062665339627314$$

Multiply 3 and 11 to get 33.

$$\frac{33}{3}+3\times 0.48480962024633706\times 2.062665339627314$$

Divide 33 by 3 to get 11.

$$11+3\times 0.48480962024633706\times 2.062665339627314$$

Multiply 3 and 0.48480962024633706 to get 1.45442886073901118.

$$11+1.45442886073901118\times 2.062665339627314$$

Multiply 1.45442886073901118 and 2.062665339627314 to get 2.99999999999999987246512207937052.

$$11+2.99999999999999987246512207937052$$

Add 11 and 2.99999999999999987246512207937052 to get 13.99999999999999987246512207937052.

$$13.99999999999999987246512207937052$$