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Bài 7. Biến đổi thành tích các biểu thức sau
a) \(1 – \sin x\); b) \(1 + \sin x\);
c) \(1 + 2\cos x\); d) \(1 – 2\sin x\)
a) \(1 – \sin x = \sin \frac{\pi }{2} – \sin x = 2\cos \frac{\frac{\pi }{2}+x}{2}\sin \frac{\frac{\pi}{2}-x}{2}\)
\(= 2 \cos \left ( \frac{\pi }{4} +\frac{x}{2}\right )\sin\left ( \frac{\pi }{4} -\frac{x}{2}\right )\)
b) \(1 + \sin x = \sin \frac{\pi }{2} + \sin x = 2\sin \left ( \frac{\pi }{4} +\frac{x}{2}\right )\cos \left ( \frac{\pi }{4} -\frac{x}{2}\right )\)
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c) \(1 + 2\cos x = 2( \frac{1}{2} + \cos x) = 2(\cos \frac{\pi}{3} + \cos x) \)
\(= 4\cos \left ( \frac{\pi }{6} +\frac{x}{2}\right )\cos \left ( \frac{\pi }{6} -\frac{x}{2}\right )\)
d) \(1 – 2\sin x = 2( \frac{1}{2} – \sin x) = 2(\sin \frac{\pi}{6} – \sin x)\)
\(= 4\cos \left ( \frac{\pi }{12} +\frac{x}{2}\right )\sin \left ( \frac{\pi }{12} -\frac{x}{2}\right )\)