Solve 1+2sin(10)/sin(20)cos(10)

$$\frac{ 1+2 \sin ( 10 ) }{ \sin ( 20 ) \cos ( 10 ) }$$

Evaluate

$$\frac{842060222083662912500000000000}{210515055520915700986969289681}\approx 4$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1 + 2 \cdot 0.17364817766693033}{0.3420201433256687 \cdot 0.984807753012208}$$

Multiply 2 and 0.17364817766693033 to get 0.34729635533386066.

$$\frac{1+0.34729635533386066}{0.3420201433256687\times 0.984807753012208}$$

Add 1 and 0.34729635533386066 to get 1.34729635533386066.

$$\frac{1.34729635533386066}{0.3420201433256687\times 0.984807753012208}$$

Multiply 0.3420201433256687 and 0.984807753012208 to get 0.3368240888334651215791508634896.

$$\frac{1.34729635533386066}{0.3368240888334651215791508634896}$$

Expand \frac{1.34729635533386066}{0.3368240888334651215791508634896} by multiplying both numerator and the denominator by 10000000000000000000000000000000.

$$\frac{13472963553338606600000000000000}{3368240888334651215791508634896}$$

Reduce the fraction \frac{13472963553338606600000000000000}{3368240888334651215791508634896} to lowest terms by extracting and canceling out 16.

$$\frac{842060222083662912500000000000}{210515055520915700986969289681}$$

Factor

$$\frac{383 \cdot 175887252654551 \cdot 2 ^ {11} \cdot 5 ^ {14}}{179 \cdot 443 \cdot 2399 \cdot 25693 \cdot 57915859 \cdot 743676121} = 4\frac{140737488355328}{2.1051505552091574 \times 10^{29}} = 4.000000000000001$$