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Chứng minh rằng với mọi \(\alpha \), ta luôn có
a) \(\sin (\alpha + {\pi \over 2}) = \cos \alpha \);
b) \({\rm{cos}}(\alpha + {\pi \over 2}) = – \sin \alpha \);
c) \(\tan (\alpha + {\pi \over 2}) = – \cot \alpha \);
d) \(\cot (\alpha + {\pi \over 2}) = – \tan \alpha \).
Gợi ý làm bài
Advertisements (Quảng cáo)
a) \(\sin (\alpha + {\pi \over 2}) = \sin ({\pi \over 2} – ( – \alpha )) = c{\rm{os( – }}\alpha {\rm{) = cos}}\alpha \)
b) \({\rm{cos}}(\alpha + {\pi \over 2}) = c{\rm{os(}}{\pi \over 2} – ( – \alpha ) = \sin ( – \alpha ) = – \sin \alpha \)
c) \(\tan (\alpha + {\pi \over 2}) = {{\sin (\alpha + {\pi \over 2})} \over {\cos (\alpha + {\pi \over 2})}} = {{\cos \alpha } \over { – \sin \alpha }} = – \cot \alpha \)
d) \(\cot (\alpha + {\pi \over 2}) = {{\cos (\alpha + {\pi \over 2})} \over {\sin (\alpha + {\pi \over 2})}} = {{ – \sin \alpha } \over {\cos \alpha }} = – \tan \alpha \)