Toán Lớp 10: Công thức rút gọn
sinx+ cosx= √2 ……………= √2……………
sinx- cosx= √2 ……………= √2……………
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Toán Lớp 10: Công thức rút gọn
sinx+ cosx= √2 ……………= √2……………
sinx- cosx= √2 ……………= √2……………
Comments ( 1 )
\sin x + \cos x\\
= \sqrt 2 \left( {\dfrac{{\sqrt 2 }}{2}\sin x + \dfrac{{\sqrt 2 }}{2}\cos x} \right)\\
= \sqrt 2 \left( {\cos \dfrac{\pi }{4}\sin x + \sin \dfrac{\pi }{4}\cos x} \right) = \sqrt 2 \sin \left( {x + \dfrac{\pi }{4}} \right)\\
= \sqrt 2 \left( {\cos x\cos \dfrac{\pi }{4} + \sin x\sin \dfrac{\pi }{4}} \right) = \sqrt 2 \cos \left( {x – \dfrac{\pi }{4}} \right)\\
\sin x – \cos x\\
= \sqrt 2 \left( {\dfrac{{\sqrt 2 }}{2}\sin x – \dfrac{{\sqrt 2 }}{2}\cos x} \right) = \sqrt 2 \left( {\sin x\cos \dfrac{\pi }{4} – \cos x\sin \dfrac{\pi }{4}} \right)\\
= \sqrt 2 \sin \left( {x – \dfrac{\pi }{4}} \right)\\
= – \sqrt 2 \left( {\cos x\cos \dfrac{\pi }{4} – \sin x.\sin \dfrac{\pi }{4}} \right) = – \sqrt 2 \cos \left( {x + \dfrac{\pi }{4}} \right)
\end{array}$