AP EAMCET · Maths · Trigonometric Equations
\(\sin \left(\frac{5 \pi}{3}\right)+\sec \left(\frac{13 \pi}{3}\right)=\)
- A \(2-\frac{\sqrt{3}}{2}\)
- B \(2+\frac{\sqrt{3}}{2}\)
- C \(\sqrt{3}+\frac{1}{\sqrt{2}}\)
- D \(\sqrt{3}-\frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(2-\frac{\sqrt{3}}{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \sin & \left(\frac{5 \pi}{3}\right)+\sec \left(\frac{13 \pi}{3}\right) \\ = & \sin \left(2 \pi-\frac{\pi}{3}\right)+\sec \left(4 \pi+\frac{\pi}{3}\right) \\ = & -\sin \frac{\pi}{3}+\sec \frac{\pi}{3}=-\frac{\sqrt{3}}{2}+2=2-\frac{\sqrt{3}}{2} \end{aligned}\)…
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