Solve cos50^circcos5^circ+sin50^circsin5^circ

$$\cos 50 ^ { \circ } \cos 5 ^ { \circ } + \sin 50 ^ { \circ } \sin 5 ^ { \circ }$$

Evaluate

$$0.70710678118654757124527778427296$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.6427876096865394 \cdot 0.9961946980917455 + 0.766044443118978 \cdot 0.08715574274765817$$

Multiply 0.6427876096865394 and 0.9961946980917455 to get 0.6403416087687968628925976005227.

$$0.6403416087687968628925976005227+0.766044443118978\times 0.08715574274765817$$

Multiply 0.766044443118978 and 0.08715574274765817 to get 0.06676517241775070835268018375026.

$$0.6403416087687968628925976005227+0.06676517241775070835268018375026$$

Add 0.6403416087687968628925976005227 and 0.06676517241775070835268018375026 to get 0.70710678118654757124527778427296.

$$0.70710678118654757124527778427296$$

Factor

$$\frac{245523187911995684460165897317 \cdot 3 ^ {2}}{2 ^ {27} \cdot 5 ^ {32}} = 0.7071067811865476$$