TS EAMCET · Maths · Trigonometric Equations
The number of all the possible integral values of \(n>2\) such that \(\sin \frac{\pi}{2 n}+\cos \frac{\pi}{2 n}=\frac{\sqrt{n}}{2}\) is
- A 5
- B 4
- C 3
- D infinity
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
Given, \[ \sin \frac{\pi}{2 n}+\cos \frac{\pi}{2 n}=\frac{\sqrt{n}}{2} \] Squaring both sides \[ \left(\sin \frac{\pi}{2 n}+\cos \frac{\pi}{2 n}\right)^2=\frac{n}{4} \]…
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