Question

calcule o cos de 105°

Answer 1

$Ola'~~~\mathbb{ISABELLA} \\ \\ sen105\° \\ \\ sen(60+45)~~---\ \textgreater \ por~indentidade~trigonometrica~temos \\ sen(a+b)=sena.cosb+cosa.senb \\ \\ sen(60+45)=sen60.cos45+cos60.sen45 ~=\ \textgreater \ \begin{cases}sen60\°= \frac{ \sqrt{3} }{2} \\ cos45\°= \frac{ \sqrt{2} }{2} \\ cos60\°= \frac{1}{2} \\ sen45\°= \frac{ \sqrt{2} }{2} \end{cases}\\ \\ sen(60+45)= \frac{ \sqrt{3} }{2}. \frac{ \sqrt{2} }{2}+ \frac{1}{2}. \frac{ \sqrt{2} }{2} \\ \\ sen(60+45)= \frac{ \sqrt{6} }{4} + \frac{ \sqrt{2} }{4}$

$sen(60+45)= \frac{ \sqrt{6}+ \sqrt{2} }{4} \\ \\ \boxed{\boxed{sen105\°= \frac{ \sqrt{6}+ \sqrt{2} }{4}}} \\ \\ \mathbb{iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii} \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$