Solve frac{sin70^{circ}}{cos70^circ}*cos10^circ*2sin(10^circ)/cos20^circ

$$\frac { \sin 70 ^ { \circ } } { \cos 70 ^ { \circ } } \cdot \cos 10 ^ { \circ } \cdot 2 \frac { \sin ( 10 ^ { \circ } ) } { \cos 20 ^ { \circ } }$$

Evaluate

$$\frac{46886916590429284672528040662519}{17101007166283440000000000000000}\approx 2.741763461$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.9396926207859083}{0.3420201433256688} \cdot 0.9979202891093386$$

Expand \frac{0.9396926207859083}{0.3420201433256688} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{9396926207859083}{3420201433256688}\times 0.9979202891093386$$

Convert decimal number 0.9979202891093386 to fraction \frac{4989601445546693}{10000000000}. Reduce the fraction \frac{4989601445546693}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{9396926207859083}{3420201433256688}\times \frac{4989601445546693}{5000000000000000}$$

Multiply \frac{9396926207859083}{3420201433256688} times \frac{4989601445546693}{5000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9396926207859083\times 4989601445546693}{3420201433256688\times 5000000000000000}$$

Do the multiplications in the fraction \frac{9396926207859083\times 4989601445546693}{3420201433256688\times 5000000000000000}.

$$\frac{46886916590429284672528040662519}{17101007166283440000000000000000}$$