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TS EAMCET · Maths · Trigonometric Ratios & Identities

Let \(\alpha\) be the period of \(3 \sin \frac{\pi x}{3}-\cos \frac{\pi x}{2}+\tan \frac{\pi x}{4}, \beta\) be the period of \(\sin ^2\left(\frac{\pi}{7}+\frac{x}{4}\right)-\sin ^2\left(\frac{\pi}{7}-\frac{x}{4}\right)\), and \(\gamma\) be the period of \(\cos ^4 x+\sin ^4 x\). Then \(\frac{\alpha \gamma}{\beta}=\)

  1. A \(\frac{3}{2}\)
  2. B \(\frac{3}{4}\)
  3. C 3
  4. D 6
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{3}{2}\)

Step-by-step Solution

Detailed explanation

Period of \(3 \sin \frac{\pi x}{3}-\cos \frac{\pi x}{2}+\tan \frac{\pi x}{4}\) is \(12(\alpha)\), period of \(\sin ^2\left(\frac{\pi}{7}+\frac{x}{4}\right)-\sin ^2 \frac{\pi}{4}-\frac{x}{4}\) is \(4 \times \pi(\beta)\) and period of \(\cos ^4(x)\) \(+\sin ^4(\mathrm{x})\) is…