Câu 6.32 trang 200 SBT Đại số 10 Nâng cao

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

Giải:

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

d) \( - 2\sin \alpha ;\)

e) 0;                 f) 0

g) \(2\cos \alpha \)

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