Solve 2sin(80)-sin(30+10)/cos(40)

$$\frac{ 2 \sin ( 80 ) - \sin ( 30+10 ) }{ \cos ( 40 ) }$$

Evaluate

$$\frac{4422759654459589}{2553481477063260}\approx 1.732050808$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{2 \cdot 0.984807753012208 - 0.6427876096865393}{0.766044443118978}$$

Multiply 2 and 0.984807753012208 to get 1.969615506024416.

$$\frac{1.969615506024416-0.6427876096865393}{0.766044443118978}$$

Subtract 0.6427876096865393 from 1.969615506024416 to get 1.3268278963378767.

$$\frac{1.3268278963378767}{0.766044443118978}$$

Expand \frac{1.3268278963378767}{0.766044443118978} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{13268278963378767}{7660444431189780}$$

Reduce the fraction \frac{13268278963378767}{7660444431189780} to lowest terms by extracting and canceling out 3.

$$\frac{4422759654459589}{2553481477063260}$$

Factor

$$\frac{107 \cdot 167 \cdot 247510193881}{5 \cdot 4728669401969 \cdot 2 ^ {2} \cdot 3 ^ {3}} = 1\frac{1869278177396329}{2553481477063260} = 1.7320508075688772$$