Đáp án:

$4\cos x.\cos\dfrac x2\cos\dfrac{5x}2$

Giải thích các bước giải:

$\cos x+\cos 2x+\cos 3x+\cos 4x$

$=(\cos x+\cos 4x)+(\cos 2x+\cos 3x)$

$=2\cos\dfrac{x+4x}2\cos\dfrac{4x-x}2+2\cos\dfrac{2x+3x}2\cos\dfrac{3x-2x}2$

$=2\cos\dfrac{5x}2\cos\dfrac{3x}2+2\cos\dfrac{5x}2\cos\dfrac x2$

$=2\cos\dfrac{5x}2\left(\cos\dfrac{3x}2+\cos\dfrac x2\right)$

$=2\cos\dfrac{5x}2.2\cos\dfrac{\dfrac{3x}2+\dfrac x2}2\cos\dfrac{\dfrac{3x}2-\dfrac x2}2$

$=4\cos\dfrac{5x}2\cos x.\cos\dfrac x2$

$=4\cos x.\cos\dfrac x2\cos\dfrac{5x}2$