TS EAMCET · Maths · Functions
If the period of the function \(f(x)=\sin 5 x \cos 3 x\) is \(\alpha\), then \(\cos \alpha=\)
- A 1
- B \(\frac{1}{\sqrt{2}}\)
- C \(-\frac{1}{2}\)
- D -1
Answer & Solution
Correct Answer
(D) -1
Step-by-step Solution
Detailed explanation
We have, \(f(x)=\sin 5 x \cdot \cos 3 x\). \[ =\frac{1}{2}(2 \sin 5 x \cdot \cos 3 x)=\frac{1}{2}(\sin 8 x+\sin 2 x) \] Clearly, \(\sin 8 x\) is periodic with period \(\frac{2 \pi}{8}=\frac{\pi}{4}\) and \(\sin 2 x\) is periodic with period \(\frac{2 \pi}{2}=\pi\).…
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