Cho sin a = √ 5 /3 . Tính cos 2 a sin a .

7/19

Cho \(\sin a = \frac{{\sqrt 5 }}{3}\). Tính \(\cos 2a\sin a\).

\(\frac{{ - \sqrt 5 }}{9}\).

\(\frac{{17\sqrt 5 }}{{27}}\).

\(\frac{{ - \sqrt 5 }}{{27}}\).

\(\frac{{\sqrt 5 }}{{27}}\).

Giải thích

Chọn C

Ta có \(B = \cos 2a\sin a = \left( {1 - 2{{\sin }^2}a} \right)\sin a = \sin a - 2{\sin ^3}a\) mà \(\sin a = \frac{{\sqrt 5 }}{3}\)

Suy ra \(B = \frac{{\sqrt 5 }}{3} - 2\frac{{5\sqrt 5 }}{{27}} = \frac{{9\sqrt 5 - 10\sqrt 5 }}{{27}} = \frac{{ - \sqrt 5 }}{{27}}\).