Rút gọn biểu thức sau: B = sin ( 5 π/2 − x ) − cos ( 11 π/2 − x ) − 3 sin ( x − 5 π ) + tan ( 7 π/2 − x ) tan ( − x ) .
Giải thích
\(B = \sin \left( {\frac{{5\pi }}{2} - x} \right) - \cos \left( {\frac{{11\pi }}{2} - x} \right) - 3\sin \left( {x - 5\pi } \right) + \tan \left( {\frac{{7\pi }}{2} - x} \right)\tan \left( { - x} \right)\)
\( = \sin \left( {2\pi + \frac{\pi }{2} - x} \right) - \cos \left( {6\pi - \frac{\pi }{2} - x} \right) - 3\sin \left( {x + \pi - 6\pi } \right) + \tan \left( {3\pi + \frac{\pi }{2} - x} \right)\tan \left( { - x} \right)\)
\( = \sin \left( {\frac{\pi }{2} - x} \right) - \cos \left( {\frac{\pi }{2} + x} \right) - 3\sin \left( {x + \pi } \right) - \tan \left( {\frac{\pi }{2} - x} \right)\tan x\)
\( = \cos x + \sin x + 3\sin x - \cot x\tan x\)
\( = \cos x + 4\sin x - 1\).