Cho biểu thức:\(C = {\mathop{\rm s}\nolimits} {\rm{inx}} + \cos x - \sin \left( {x - \frac{\pi }{6}} \right) + \cos \left( {x - \frac{\pi }{6}} \right)\). Biết biểu thức C có dạng \(\sqrt a \

Đáp án: 6

\(C = {\mathop{\rm s}\nolimits} {\rm{inx}} + \cos x - \sin \left( {x - \frac{\pi }{6}} \right) + \cos \left( {x - \frac{\pi }{6}} \right)\)

\( = \sqrt 2 \cos \left( {x - \frac{\pi }{4}} \right) + \cos \left( {x + \frac{\pi }{3}} \right) + \cos \left( {x - \frac{\pi }{6}} \right)\)

\( = \sqrt 2 \cos \left( {x - \frac{\pi }{4}} \right) + 2\cos \left( {x + \frac{\pi }{{12}}} \right) \cdot \cos \frac{\pi }{4}\)

\( = \sqrt 2 \left[ {\cos \left( {x - \frac{\pi }{4}} \right) + \cos \left( {x + \frac{\pi }{{12}}} \right)} \right] = 2\sqrt 2 \cos \left( {x - \frac{\pi }{{12}}} \right) \cdot \cos \frac{\pi }{6}\)

\( = \sqrt 6 \cos \left( {x - \frac{\pi }{{12}}} \right)\).

Vậy a = 6.