Solve frac{5cos0-2sin30+sqrt{3}cos30}{tan30*tan10*cos60}+3sin29sec61

$$\frac { 5 \cos 0 - 2 \sin 30 + \sqrt { 3 } \cos 30 } { \tan 30 \times \tan 10 \times \cos 60 } + 3 \sin 29 \sec 61$$

Evaluate

$$\frac{70469038504365279651920878068304187609248657239569}{573012834788426575000000000000000000000000000000}\approx 122.97986053$$

Short Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{5 \cos(0) - 2 \sin(30) + \sqrt{3} \cos(30)}{0.045841026783074126} + 3 \cdot 0.48480962024633706 \cdot 2.062665339627314$$

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

$$\frac{5\times 1-2\sin(30)+\sqrt{3}\cos(30)}{0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

Multiply 5 and 1 to get 5.

$$\frac{5-2\sin(30)+\sqrt{3}\cos(30)}{0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{5-2\times \frac{1}{2}+\sqrt{3}\cos(30)}{0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{5-1+\sqrt{3}\cos(30)}{0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

Subtract 1 from 5 to get 4.

$$\frac{4+\sqrt{3}\cos(30)}{0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{4+\sqrt{3}\times \frac{\sqrt{3}}{2}}{0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{4+\frac{\sqrt{3}\sqrt{3}}{2}}{0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{\frac{4\times 2}{2}+\frac{\sqrt{3}\sqrt{3}}{2}}{0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{\frac{4\times 2+\sqrt{3}\sqrt{3}}{2}}{0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

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

$$\frac{\frac{8+3}{2}}{0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

Do the calculations in 8+3.

$$\frac{\frac{11}{2}}{0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

Express \frac{\frac{11}{2}}{0.045841026783074126} as a single fraction.

$$\frac{11}{2\times 0.045841026783074126}+3\times 0.48480962024633706\times 2.062665339627314$$

Multiply 2 and 0.045841026783074126 to get 0.091682053566148252.

$$\frac{11}{0.091682053566148252}+3\times 0.48480962024633706\times 2.062665339627314$$

Expand \frac{11}{0.091682053566148252} by multiplying both numerator and the denominator by 1000000000000000000.

$$\frac{11000000000000000000}{91682053566148252}+3\times 0.48480962024633706\times 2.062665339627314$$

Reduce the fraction \frac{11000000000000000000}{91682053566148252} to lowest terms by extracting and canceling out 4.

$$\frac{2750000000000000000}{22920513391537063}+3\times 0.48480962024633706\times 2.062665339627314$$

Multiply 3 and 0.48480962024633706 to get 1.45442886073901118.

$$\frac{2750000000000000000}{22920513391537063}+1.45442886073901118\times 2.062665339627314$$

Multiply 1.45442886073901118 and 2.062665339627314 to get 2.99999999999999987246512207937052.

$$\frac{2750000000000000000}{22920513391537063}+2.99999999999999987246512207937052$$

Add \frac{2750000000000000000}{22920513391537063} and 2.99999999999999987246512207937052 to get \frac{70469038504365279651920878068304187609248657239569}{573012834788426575000000000000000000000000000000}.

$$\frac{70469038504365279651920878068304187609248657239569}{573012834788426575000000000000000000000000000000}$$