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AP EAMCET · Maths · Trigonometric Equations

\(\sin \left(\frac{5 \pi}{3}\right)+\sec \left(\frac{13 \pi}{3}\right)=\)

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

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

\(\begin{aligned} \sin & \left(\frac{5 \pi}{3}\right)+\sec \left(\frac{13 \pi}{3}\right) \\ = & \sin \left(2 \pi-\frac{\pi}{3}\right)+\sec \left(4 \pi+\frac{\pi}{3}\right) \\ = & -\sin \frac{\pi}{3}+\sec \frac{\pi}{3}=-\frac{\sqrt{3}}{2}+2=2-\frac{\sqrt{3}}{2} \end{aligned}\)…