Solve 2/3csc^{2}58^{circ}-2/3cot50^{circ}tan32^{circ}-5/3tan13^{circ}tan37^circtan45^circtan53^circtan77^circ

$$\frac { 2 } { 3 } \csc ^ { 2 } 58 ^ { \circ } - \frac { 2 } { 3 } \cot 50 ^ { \circ } \tan 32 ^ { \circ } - \frac { 5 } { 3 } \tan 13 ^ { \circ } \tan 37 ^ { \circ } \tan 45 ^ { \circ } \tan 53 ^ { \circ } \tan 77 ^ { \circ }$$

Evaluate

$$-\frac{204233241970690108380265980315993364718219233621345501520105717}{187500000000000000000000000000000000000000000000000000000000000}\approx -1.089243957$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{2}{3} 1.1791784033620962 ^ {2} - \frac{2}{3} 0.83909963117728 \cdot 0.6248693519093275 - \frac{5}{3} 0.23086819112556312 \cdot 0.7535540501027942 \tan(45) 1.3270448216204098 \cdot 4.331475874284157$$

Calculate 1.1791784033620962 to the power of 2 and get 1.39046170695558244682785085805444.

$$\frac{2}{3}\times 1.39046170695558244682785085805444-\frac{2}{3}\times 0.83909963117728\times 0.6248693519093275-0.23086819112556312\times 0.7535540501027942\times 1.3270448216204098\times 4.331475874284157\times \frac{5}{3}\tan(45)$$

Multiply \frac{2}{3} and 1.39046170695558244682785085805444 to get \frac{11587180891296520390232090483787}{12500000000000000000000000000000}.

$$\frac{11587180891296520390232090483787}{12500000000000000000000000000000}-\frac{2}{3}\times 0.83909963117728\times 0.6248693519093275-0.23086819112556312\times 0.7535540501027942\times 1.3270448216204098\times 4.331475874284157\times \frac{5}{3}\tan(45)$$

Multiply \frac{2}{3} and 0.83909963117728 to get \frac{2622186347429}{4687500000000}.

$$\frac{11587180891296520390232090483787}{12500000000000000000000000000000}-\frac{2622186347429}{4687500000000}\times 0.6248693519093275-0.23086819112556312\times 0.7535540501027942\times 1.3270448216204098\times 4.331475874284157\times \frac{5}{3}\tan(45)$$

Multiply \frac{2622186347429}{4687500000000} and 0.6248693519093275 to get \frac{655409553401378361768297599}{1875000000000000000000000000}.

$$\frac{11587180891296520390232090483787}{12500000000000000000000000000000}-\frac{655409553401378361768297599}{1875000000000000000000000000}-0.23086819112556312\times 0.7535540501027942\times 1.3270448216204098\times 4.331475874284157\times \frac{5}{3}\tan(45)$$

Subtract \frac{655409553401378361768297599}{1875000000000000000000000000} from \frac{11587180891296520390232090483787}{12500000000000000000000000000000} to get \frac{21653351605861993935330319471361}{37500000000000000000000000000000}.

$$\frac{21653351605861993935330319471361}{37500000000000000000000000000000}-0.23086819112556312\times 0.7535540501027942\times 1.3270448216204098\times 4.331475874284157\times \frac{5}{3}\tan(45)$$

Multiply 0.23086819112556312 and 0.7535540501027942 to get 0.173971660462574058618835360469904.

$$\frac{21653351605861993935330319471361}{37500000000000000000000000000000}-0.173971660462574058618835360469904\times 1.3270448216204098\times 4.331475874284157\times \frac{5}{3}\tan(45)$$

Multiply 0.173971660462574058618835360469904 and 1.3270448216204098 to get 0.2308681911255630918923293573561541517892450466592.

$$\frac{21653351605861993935330319471361}{37500000000000000000000000000000}-0.2308681911255630918923293573561541517892450466592\times 4.331475874284157\times \frac{5}{3}\tan(45)$$

Multiply 0.2308681911255630918923293573561541517892450466592 and 4.331475874284157 to get 1.0000000000000002497821362485529547670983015475883056048643382944.

$$\frac{21653351605861993935330319471361}{37500000000000000000000000000000}-1.0000000000000002497821362485529547670983015475883056048643382944\times \frac{5}{3}\tan(45)$$

Multiply 1.0000000000000002497821362485529547670983015475883056048643382944 and \frac{5}{3} to get \frac{104166666666666692685639192557599454906073077873781833840035239}{62500000000000000000000000000000000000000000000000000000000000}.

$$\frac{21653351605861993935330319471361}{37500000000000000000000000000000}-\frac{104166666666666692685639192557599454906073077873781833840035239}{62500000000000000000000000000000000000000000000000000000000000}\tan(45)$$

Get the value of \tan(45) from trigonometric values table.

$$\frac{21653351605861993935330319471361}{37500000000000000000000000000000}-\frac{104166666666666692685639192557599454906073077873781833840035239}{62500000000000000000000000000000000000000000000000000000000000}\times 1$$

Multiply \frac{104166666666666692685639192557599454906073077873781833840035239}{62500000000000000000000000000000000000000000000000000000000000} and 1 to get \frac{104166666666666692685639192557599454906073077873781833840035239}{62500000000000000000000000000000000000000000000000000000000000}.

$$\frac{21653351605861993935330319471361}{37500000000000000000000000000000}-\frac{104166666666666692685639192557599454906073077873781833840035239}{62500000000000000000000000000000000000000000000000000000000000}$$

Subtract \frac{104166666666666692685639192557599454906073077873781833840035239}{62500000000000000000000000000000000000000000000000000000000000} from \frac{21653351605861993935330319471361}{37500000000000000000000000000000} to get -\frac{204233241970690108380265980315993364718219233621345501520105717}{187500000000000000000000000000000000000000000000000000000000000}.

$$-\frac{204233241970690108380265980315993364718219233621345501520105717}{187500000000000000000000000000000000000000000000000000000000000}$$