Solve cos40^circ+sin40^circ/2cos20^circ

$$\frac { \cos 40 ^ { \circ } + \sin 40 ^ { \circ } } { 2 \cos 20 ^ { \circ } }$$

Evaluate

$$\frac{14088320528055173}{18793852415718168}\approx 0.749623878$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.766044443118978 + 0.6427876096865393}{2 \cdot 0.9396926207859084}$$

Add 0.766044443118978 and 0.6427876096865393 to get 1.4088320528055173.

$$\frac{1.4088320528055173}{2\times 0.9396926207859084}$$

Multiply 2 and 0.9396926207859084 to get 1.8793852415718168.

$$\frac{1.4088320528055173}{1.8793852415718168}$$

Expand \frac{1.4088320528055173}{1.8793852415718168} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{14088320528055173}{18793852415718168}$$

Factor

$$\frac{19 \cdot 741490554108167}{3 \cdot 587 \cdot 1334032681411 \cdot 2 ^ {3}} = 0.749623877873621$$