Solve frac{sqrt{6}sin(sqrt{6})}{(1+cossqrt{6})}+csc(sqrt{6})(sqrt{6}+sqrt{6}cossqrt{6})

$$\frac { \sqrt { 6 } \sin ( \sqrt { 6 } ) } { ( 1 + \cos \sqrt { 6 } ) } + \csc ( \sqrt { 6 } ) ( \sqrt { 6 } + \sqrt { 6 } \cos \sqrt { 6 } )$$

Evaluate

$$\frac{46774682580128546587454684780848440220989392573\sqrt{6}}{999543143459909500000000000000000000000000000}\approx 114.626473056$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{\sqrt{6} 0.042738639294777336}{{(1 + 0.999086286919819)}} + 23.398030833475786 {(\sqrt{6} + \sqrt{6} 0.999086286919819)}$$

Add 1 and 0.999086286919819 to get 1.999086286919819.

$$\frac{0.042738639294777336\sqrt{6}}{1.999086286919819}+23.398030833475786\left(\sqrt{6}+0.999086286919819\sqrt{6}\right)$$

Divide 0.042738639294777336\sqrt{6} by 1.999086286919819 to get \frac{5342329911847167}{249885785864977375}\sqrt{6}.

$$\frac{5342329911847167}{249885785864977375}\sqrt{6}+23.398030833475786\left(\sqrt{6}+0.999086286919819\sqrt{6}\right)$$

Combine \sqrt{6} and 0.999086286919819\sqrt{6} to get 1.999086286919819\sqrt{6}.

$$\frac{5342329911847167}{249885785864977375}\sqrt{6}+23.398030833475786\times 1.999086286919819\sqrt{6}$$

Multiply 23.398030833475786 and 1.999086286919819 to get 46.774682580128546828887660002734.

$$\frac{5342329911847167}{249885785864977375}\sqrt{6}+46.774682580128546828887660002734\sqrt{6}$$

Combine \frac{5342329911847167}{249885785864977375}\sqrt{6} and 46.774682580128546828887660002734\sqrt{6} to get \frac{46774682580128546587454684780848440220989392573}{999543143459909500000000000000000000000000000}\sqrt{6}.

$$\frac{46774682580128546587454684780848440220989392573}{999543143459909500000000000000000000000000000}\sqrt{6}$$