Question

ITEEM D PFVR ALGUÉM sabe?

Answer 1

$\left[\begin{array}{ccc}\text{sen}~15^{\circ}&\text{cos}~15^{\circ}\\-\text{sen}~15^{\circ}&\text{cos}~15^{\circ}\end{array}\right]=\text{sen}~15^{\circ}\cdot\text{cos}~15^{\circ}-(-\text{sen}~15^{\circ})\cdot\text{cos}~15^{\circ}$

$\left[\begin{array}{ccc}\text{sen}~15^{\circ}&\text{cos}~15^{\circ}\\-\text{sen}~15^{\circ}&\text{cos}~15^{\circ}\end{array}\right]=\text{sen}~15^{\circ}\cdot\text{cos}~15^{\circ}+\text{sen}~15^{\circ}\cdot\text{cos}~15^{\circ}$

Lembre-se que $\text{sen}~(a+b)=\text{sen}~a\cdot\text{cos}~b+\text{sen}~b\cdot\text{cos}~a$

Logo, $\text{sen}~15^{\circ}\cdot\text{cos}~15^{\circ}+\text{sen}~15^{\circ}\cdot\text{cos}~15^{\circ}=\text{sen}~(15^{\circ}+15^{\circ})=\text{sen}~30^{\circ}$

E $\text{sen}~30^{\circ}=\dfrac{1}{2}$, então:

$\left[\begin{array}{ccc}\text{sen}~15^{\circ}&\text{cos}~15^{\circ}\\-\text{sen}~15^{\circ}&\text{cos}~15^{\circ}\end{array}\right]=\boxed{\dfrac{1}{2}}$