Rút gọn: cos `x/5` cos `(2x)/5` cos `(4x)/5` cos `(8x)/5` 03/09/2021 Bởi Ivy Rút gọn: cos `x/5` cos `(2x)/5` cos `(4x)/5` cos `(8x)/5`
$A=\cos\dfrac{x}{5}\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}$ $A.\sin\dfrac{x}{5}=\sin\dfrac{x}{5}\cos\dfrac{x}{5}.\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}$ $=\dfrac{1}{2}\sin\dfrac{2x}{5}\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}$ $=\dfrac{1}{4}\sin\dfrac{4x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}$ $=\dfrac{1}{8}\sin\dfrac{8x}{5}\cos\dfrac{8x}{5}$ $=\dfrac{1}{16}\sin\dfrac{16x}{5}$ Vậy $A=\dfrac{\sin\dfrac{16x}{5} }{16\sin\dfrac{x}{5}}$ Bình luận
Đáp án: $\dfrac{\sin\dfrac{16x}{5}}{16\sin\dfrac{x}{5}}$ Giải thích các bước giải: $\quad \cos\dfrac x5\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}$ $= \dfrac{2\sin\dfrac x5\cos\dfrac x5\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}}{2\sin\dfrac x5}$ $= \dfrac{\sin\dfrac{2x}{5}\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}}{2\sin\dfrac x5}$ $= \dfrac{2\sin\dfrac{2x}{5}\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}}{4\sin\dfrac x5}$ $= \dfrac{\sin\dfrac{4x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}}{4\sin\dfrac x5}$ $=\dfrac{2\sin\dfrac{4x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}}{8\sin\dfrac x5}$ $= \dfrac{\sin\dfrac{8x}{5}\cos\dfrac{8x}{5}}{8\sin\dfrac x5}$ $= \dfrac{2\sin\dfrac{8x}{5}\cos\dfrac{8x}{5}}{16\sin\dfrac x5}$ $=\dfrac{\sin\dfrac{16x}{5}}{16\sin\dfrac{x}{5}}$ Bình luận
$A=\cos\dfrac{x}{5}\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}$
$A.\sin\dfrac{x}{5}=\sin\dfrac{x}{5}\cos\dfrac{x}{5}.\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}$
$=\dfrac{1}{2}\sin\dfrac{2x}{5}\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}$
$=\dfrac{1}{4}\sin\dfrac{4x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}$
$=\dfrac{1}{8}\sin\dfrac{8x}{5}\cos\dfrac{8x}{5}$
$=\dfrac{1}{16}\sin\dfrac{16x}{5}$
Vậy $A=\dfrac{\sin\dfrac{16x}{5} }{16\sin\dfrac{x}{5}}$
Đáp án:
$\dfrac{\sin\dfrac{16x}{5}}{16\sin\dfrac{x}{5}}$
Giải thích các bước giải:
$\quad \cos\dfrac x5\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}$
$= \dfrac{2\sin\dfrac x5\cos\dfrac x5\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}}{2\sin\dfrac x5}$
$= \dfrac{\sin\dfrac{2x}{5}\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}}{2\sin\dfrac x5}$
$= \dfrac{2\sin\dfrac{2x}{5}\cos\dfrac{2x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}}{4\sin\dfrac x5}$
$= \dfrac{\sin\dfrac{4x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}}{4\sin\dfrac x5}$
$=\dfrac{2\sin\dfrac{4x}{5}\cos\dfrac{4x}{5}\cos\dfrac{8x}{5}}{8\sin\dfrac x5}$
$= \dfrac{\sin\dfrac{8x}{5}\cos\dfrac{8x}{5}}{8\sin\dfrac x5}$
$= \dfrac{2\sin\dfrac{8x}{5}\cos\dfrac{8x}{5}}{16\sin\dfrac x5}$
$=\dfrac{\sin\dfrac{16x}{5}}{16\sin\dfrac{x}{5}}$