Bài tập 6.16 trang 185 SBT Toán 10

a) \(\sin \left( {\alpha  + \frac{\pi }{2}} \right) = \sin \left( {\frac{\pi }{2} - \left( { - \alpha } \right)} \right) = \cos \left( { - \alpha } \right) = \cos \alpha \)

b) \(\cos \left( {\alpha  + \frac{\pi }{2}} \right) = \cos \left( {\frac{\pi }{2} - \left( { - \alpha } \right)} \right) = \sin \left( { - \alpha } \right) =  - \sin \alpha \)

c) \(\tan \left( {\alpha  + \frac{\pi }{2}} \right) = \frac{{\sin \left( {\alpha  + \frac{\pi }{2}} \right)}}{{\cos \left( {\alpha  + \frac{\pi }{2}} \right)}} = \frac{{\cos \alpha }}{{ - \sin \alpha }} =  - \cot \alpha \)

d) \(\cot \left( {\alpha  + \frac{\pi }{2}} \right) = \frac{{\cos \left( {\alpha  + \frac{\pi }{2}} \right)}}{{\sin \left( {\alpha  + \frac{\pi }{2}} \right)}} = \frac{{ - \sin \alpha }}{{\cos \alpha }} =  - \tan \alpha \)

-- Mod Toán 10 HỌC247