Câu 6.32 trang 200 SBT Đại số 10 Nâng cao:  Đơn giản biểu thức:...

 Đơn giản biểu thức:

a) $\cos \left( {\alpha  - \dfrac{\pi }{2}} \right) + \sin \left( {\alpha  - \pi } \right);$

b) $\cos \left( {\pi  - \alpha } \right) + \sin \left( {\alpha  + \dfrac{\pi }{2}} \right);$

c) $\cos \left( {\dfrac{\pi }{2} - \alpha } \right) + \sin \left( {\dfrac{\pi }{2} - \alpha } \right) - \cos \left( {\dfrac{\pi }{2} + \alpha } \right) - \sin \left( {\dfrac{\pi }{2} + \alpha } \right)$;

d) $\cos \left( {\dfrac{{3\pi }}{2} - \alpha } \right) - \sin \left( {\dfrac{{3\pi }}{2} - \alpha } \right) + \cos \left( {\alpha  - \dfrac{{7\pi }}{2}} \right) - \sin \left( {\alpha  - \dfrac{{7\pi }}{2}} \right)$;

e) $\cos \left( {\dfrac{\pi }{2} - \alpha } \right) + \cos \left( {\pi  - \alpha } \right) + \cos \left( {\dfrac{{3\pi }}{2} - \alpha } \right) + \cos \left( {2\pi  - \alpha } \right)$;

f) $\sin \left( {\dfrac{{5\pi }}{2} - \alpha } \right) - \cos \left( {\dfrac{{13\pi }}{2} - \alpha } \right) - 3\sin \left( {\alpha  - 5\pi } \right) - 2\sin \alpha  - \cos \alpha ;$

g) $\cos \left( {5\pi  + \alpha } \right) - 2\sin \left( {\dfrac{{11\pi }}{2} - \alpha } \right) - \sin \left( {\dfrac{{11\pi }}{2} + \alpha } \right)$.

a) 0;                 b) 0;                 c) $2\sin \alpha$;

d) $- 2\sin \alpha ;$

e) 0;                 f) 0

g) $2\cos \alpha$