Chứng minh rằng với mọi α, ta luôn có:
a) \(\sin \left( {\alpha + \frac{\pi }{2}} \right) = \cos \alpha \)
b) \(\cos \left( {\alpha + \frac{\pi }{2}} \right) = - \sin \alpha \)
c) \(\tan \left( {\alpha + \frac{\pi }{2}} \right) = - \cot \alpha \)
d) \(\cot \left( {\alpha + \frac{\pi }{2}} \right) = - \tan \alpha \)
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