Solve (frac{3sin43^{circ}}{cos47^{circ}})^{2}-frac{cos37^{circ}csc53^circ}{tan5^circtan25^circtan45^circtan6}

$$( \frac { 3 \sin 43 ^ { \circ } } { \cos 47 ^ { \circ } } ) ^ { 2 } - \frac { \cos 37 ^ { \circ } \csc 53 ^ { \circ } } { \tan 5 ^ { \circ } \tan 25 ^ { \circ } \tan 45 ^ { \circ } \tan 6 }$$

Evaluate

$$-\frac{728340082593681864919164886870693080396475284953}{3248408331341743363245799673034102178169412783}\approx -224.214448524$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(\frac{3 \cdot 0.6819983600624985}{0.6819983600624985})} ^ {2} - \frac{0.7986355100472928 \cdot 1.2521356581562257}{0.08748866352592401 \cdot 0.4663076581549986 \tan(45) 0.10510423526567646}$$

Cancel out 0.6819983600624985 and 0.6819983600624985.

$$3^{2}-\frac{0.7986355100472928\times 1.2521356581562257}{0.08748866352592401\times 0.10510423526567646\times 0.4663076581549986\tan(45)}$$

Calculate 3 to the power of 2 and get 9.

$$9-\frac{0.7986355100472928\times 1.2521356581562257}{0.08748866352592401\times 0.10510423526567646\times 0.4663076581549986\tan(45)}$$

Multiply 0.7986355100472928 and 1.2521356581562257 to get 0.99999999999999997284865775078496.

$$9-\frac{0.99999999999999997284865775078496}{0.08748866352592401\times 0.10510423526567646\times 0.4663076581549986\tan(45)}$$

Multiply 0.08748866352592401 and 0.10510423526567646 to get 0.0091954290743083241548809592058046.

$$9-\frac{0.99999999999999997284865775078496}{0.0091954290743083241548809592058046\times 0.4663076581549986\tan(45)}$$

Multiply 0.0091954290743083241548809592058046 and 0.4663076581549986 to get 0.00428789899737110123948445556840501487518362487356.

$$9-\frac{0.99999999999999997284865775078496}{0.00428789899737110123948445556840501487518362487356\tan(45)}$$

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

$$9-\frac{0.99999999999999997284865775078496}{0.00428789899737110123948445556840501487518362487356\times 1}$$

Multiply 0.00428789899737110123948445556840501487518362487356 and 1 to get 0.00428789899737110123948445556840501487518362487356.

$$9-\frac{0.99999999999999997284865775078496}{0.00428789899737110123948445556840501487518362487356}$$

Expand \frac{0.99999999999999997284865775078496}{0.00428789899737110123948445556840501487518362487356} by multiplying both numerator and the denominator by 100000000000000000000000000000000000000000000000000.

$$9-\frac{99999999999999997284865775078496000000000000000000}{428789899737110123948445556840501487518362487356}$$

Reduce the fraction \frac{99999999999999997284865775078496000000000000000000}{428789899737110123948445556840501487518362487356} to lowest terms by extracting and canceling out 132.

$$9-\frac{757575757575757555188377083928000000000000000000}{3248408331341743363245799673034102178169412783}$$

Subtract \frac{757575757575757555188377083928000000000000000000}{3248408331341743363245799673034102178169412783} from 9 to get -\frac{728340082593681864919164886870693080396475284953}{3248408331341743363245799673034102178169412783}.

$$-\frac{728340082593681864919164886870693080396475284953}{3248408331341743363245799673034102178169412783}$$