Solve 6quad2cos10^circ-sin20^circ/sin70^circ

$$6 \quad \frac { 2 \cos 10 ^ { \circ } - \sin 20 ^ { \circ } } { \sin 70 ^ { \circ } }$$

Evaluate

$$\frac{97655721761924838}{9396926207859083}\approx 10.392304845$$

Solution Steps

Evaluate trigonometric functions in the problem

$$6 \frac{2 \cdot 0.984807753012208 - 0.3420201433256687}{0.9396926207859083}$$

Multiply 2 and 0.984807753012208 to get 1.969615506024416.

$$6\times \frac{1.969615506024416-0.3420201433256687}{0.9396926207859083}$$

Subtract 0.3420201433256687 from 1.969615506024416 to get 1.6275953626987473.

$$6\times \frac{1.6275953626987473}{0.9396926207859083}$$

Expand \frac{1.6275953626987473}{0.9396926207859083} by multiplying both numerator and the denominator by 10000000000000000.

$$6\times \frac{16275953626987473}{9396926207859083}$$

Express 6\times \frac{16275953626987473}{9396926207859083} as a single fraction.

$$\frac{6\times 16275953626987473}{9396926207859083}$$

Multiply 6 and 16275953626987473 to get 97655721761924838.

$$\frac{97655721761924838}{9396926207859083}$$

Factor

$$\frac{2 \cdot 37 \cdot 53 \cdot 283 \cdot 1511 \cdot 2156629 \cdot 3 ^ {3}}{87553 \cdot 107328432011} = 10\frac{3686459683333992}{9396926207859084} = 10.392304845413262$$