Solve A=frac{sqrt{6}+cos20^{circ}+cos160^{circ}}{sin^240^circ+cos^2140^circ}=

$$A = \frac { \sqrt { 6 } + \cos 20 ^ { \circ } + \cos 160 ^ { \circ } } { \sin ^ { 2 } 40 ^ { \circ } + \cos ^ { 2 } 140 ^ { \circ } } =$$

Solve for A

$$A=\frac{-12500000000000000000000000000000\sqrt{6}-1250000000000000}{2170602220836627194367144128049}\approx -14.10604923$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$A = \frac{\sqrt{6} + 0.9396926207859084 + -0.9396926207859083}{0.6427876096865393 ^ {2} + -0.7660444431189779 ^ {2}}$$

Subtract 0.9396926207859083 from 0.9396926207859084 to get 0.0000000000000001.

$$A=\frac{\sqrt{6}+0.0000000000000001}{0.6427876096865393^{2}-0.7660444431189779^{2}}$$

Calculate 0.6427876096865393 to the power of 2 and get 0.41317591116653479173440361044449.

$$A=\frac{\sqrt{6}+0.0000000000000001}{0.41317591116653479173440361044449-0.7660444431189779^{2}}$$

Calculate 0.7660444431189779 to the power of 2 and get 0.58682408883346496728377514068841.

$$A=\frac{\sqrt{6}+0.0000000000000001}{0.41317591116653479173440361044449-0.58682408883346496728377514068841}$$

Subtract 0.58682408883346496728377514068841 from 0.41317591116653479173440361044449 to get -0.17364817766693017554937153024392.

$$A=\frac{\sqrt{6}+0.0000000000000001}{-0.17364817766693017554937153024392}$$

Multiply both numerator and denominator by -1.

$$A=\frac{-\sqrt{6}-0.0000000000000001}{0.17364817766693017554937153024392}$$

Divide each term of -\sqrt{6}-0.0000000000000001 by 0.17364817766693017554937153024392 to get \frac{-\sqrt{6}}{0.17364817766693017554937153024392}+\frac{-0.0000000000000001}{0.17364817766693017554937153024392}.

$$A=\frac{-\sqrt{6}}{0.17364817766693017554937153024392}+\frac{-0.0000000000000001}{0.17364817766693017554937153024392}$$

Divide -\sqrt{6} by 0.17364817766693017554937153024392 to get -\frac{12500000000000000000000000000000}{2170602220836627194367144128049}\sqrt{6}.

$$A=-\frac{12500000000000000000000000000000}{2170602220836627194367144128049}\sqrt{6}+\frac{-0.0000000000000001}{0.17364817766693017554937153024392}$$

Expand \frac{-0.0000000000000001}{0.17364817766693017554937153024392} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$A=-\frac{12500000000000000000000000000000}{2170602220836627194367144128049}\sqrt{6}+\frac{-10000000000000000}{17364817766693017554937153024392}$$

Reduce the fraction \frac{-10000000000000000}{17364817766693017554937153024392} to lowest terms by extracting and canceling out 8.

$$A=-\frac{12500000000000000000000000000000}{2170602220836627194367144128049}\sqrt{6}-\frac{1250000000000000}{2170602220836627194367144128049}$$

Assign A

$$A≔\frac{-12500000000000000000000000000000\sqrt{6}-1250000000000000}{2170602220836627194367144128049}$$