Question

Tính giá trị biểu thức

\(A=sin\dfrac{\pi}{9}-sin\dfrac{5\pi}{9}+sin\dfrac{7\pi}{9}\)

Answer 1

\(A=sin\left(\dfrac{7}{9}pi\right)+sin\left(\dfrac{pi}{9}\right)-sin\left(\dfrac{5}{9}pi\right)\)

\(=2\cdot sin\left(\dfrac{1}{2}\cdot\dfrac{8}{9}pi\right)\cdot cos\left(\dfrac{1}{2}\cdot\dfrac{6}{9}pi\right)-sin\left(\dfrac{5}{9}pi\right)\)

\(=sin\left(\dfrac{4}{9}pi\right)-sin\left(\dfrac{5}{9}pi\right)\)

\(=2\cdot cos\left(\dfrac{\dfrac{4}{9}pi+\dfrac{5}{9}pi}{2}\right)\cdot sin\left(\dfrac{\dfrac{4}{9}pi-\dfrac{5}{9}pi}{2}\right)\)

=0