Question

Determine o valor de X em :
X= Sen45° - Sen165° + Cos30° + Cos150°​

Answer 1

Explicação passo-a-passo:

sen 165° = sen (90° + 75°)

sen 165° = sen 90°.cos 75° + sen 75°.cos 90°

sen 165° = 1.cos 75° + sen 75°.0

sen 165° = cos 75°

cos 75° = cos (45° + 30°)

cos 75° = cos 45°.cos 30° - sen 45°.sen 30°

cos 75° = (√2/2).(√3/2) - (√2/2).(1/2)

cos 75° = (√6/4) - (√2/4)

cos 75° = [(√6 - √2)/4]

cos 150° = cos (180° - 30°)

cos 150° = cos 180°.cos 30° + sen 180°.sen 30°

cos 150° = - 1.cos 30° + 0.sen 30°

cos 150° = - cos 30°

$\frac{\sqrt{2}}{2} - \frac{\sqrt{6} - \sqrt{2}}{4} + cos 30 - cos 30 \\\\\ x = \frac{2\sqrt{2} - (\sqrt{6} - \sqrt{2})}{4} \\\\\ x = \frac{- 4\sqrt{3} + 4}{4} \\\\\ x = 1 - \sqrt{3}$

Espero ter ajudado.