Question

calcule sem 75° - cos 105°?

Answer 1

sen (a+b) = sen a . cos b + sen b . cos a
sen (30 + 45) = sen 30° . cos 45° + sen 45° . cos 30°
sen (75°) = $\frac{1}{2}. \frac{ \sqrt{2} }{2} + \frac{ \sqrt{3} }{2} . \frac{ \sqrt{2} }{2}$

sen 75° = $\frac{ \sqrt{2} }{4} + \frac{ \sqrt{6} }{4}$

sen 75° = $\frac{ \sqrt{2} + \sqrt{6} }{4}$

cos (a+b) = cos a . cos b - sen a . sen b
cos ( 45 + 60) = cos 45° . cos 60° - sen 45° . sen 60°
cos (105°) = $\frac{ \sqrt{2} }{2} . \frac{1}{2} - \frac{ \sqrt{2} }{2} . \frac{ \sqrt{3} }{2}$

cos 105º = $\frac{ \sqrt{2} }{4} - \frac{ \sqrt{6} }{4}$

cos 105° = $\frac{ \sqrt{2} - \sqrt{6} }{4}$

Sen 75° - cos 105° = $\frac{ \sqrt{2} + \sqrt{6} }{4} - \frac{ \sqrt{2} - \sqrt{6} }{4}$

Sen 75° - cos 105° = $\frac{ \sqrt{2} - \sqrt{2} + \sqrt{6} + \sqrt{6} }{4} = \frac{2 \sqrt{6} }{4} <strong>= \frac{ \sqrt{6} }{2}$