Solve sin70^circ-cos40^circ/cos50^circ-sin20^circ

$$\frac { \sin 70 ^ { \circ } - \cos 40 ^ { \circ } } { \cos 50 ^ { \circ } - \sin 20 ^ { \circ } }$$

Evaluate

$$\frac{1736481776669303}{3007674663608707}\approx 0.577350269$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.9396926207859083 - 0.766044443118978}{0.6427876096865394 - 0.3420201433256687}$$

Subtract 0.766044443118978 from 0.9396926207859083 to get 0.1736481776669303.

$$\frac{0.1736481776669303}{0.6427876096865394-0.3420201433256687}$$

Subtract 0.3420201433256687 from 0.6427876096865394 to get 0.3007674663608707.

$$\frac{0.1736481776669303}{0.3007674663608707}$$

Expand \frac{0.1736481776669303}{0.3007674663608707} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{1736481776669303}{3007674663608707}$$

Factor

$$\frac{19 \cdot 91393777719437}{29 \cdot 1409 \cdot 4937 \cdot 14909351} = 0.5773502691896254$$