Question

O valor de cos(105°) é:​

Answer 1

Resposta:

\cos(105^\circ) = \cos(60^\circ + 45^\circ) = \\\\ \cos(60^\circ) \times \cos(45^\circ) - \sin(60^\circ) \times \sin(45^\circ) \\\\ \frac{1}{2} \times \frac{ \sqrt{2} }{2} - \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{2} }{2} \\ \\ \frac{ \sqrt{2} }{4 } - \frac{ \sqrt{6} }{4} \\ \\ \boxed{\cos(105^\circ) = \frac{ \sqrt{2} - \sqrt{6} }{4}}

Explicação passo-a-passo: