AP EAMCET · Maths · Trigonometric Equations
The general solution of the trigonometric equation \((\sqrt{3}-1) \sin \theta+(\sqrt{3}+1) \cos \theta=2\) is
- A \(2 n \pi \pm \frac{\pi}{4}+\frac{\pi}{12}\)
- B \(n \pi+(-1)^n \frac{\pi}{4}+\frac{\pi}{12}\)
- C \(2 n \pi \pm \frac{\pi}{4}-\frac{\pi}{12}\)
- D \(n \pi+(-1)^n \frac{\pi}{4}-\frac{\pi}{12}\)
Answer & Solution
Correct Answer
(A) \(2 n \pi \pm \frac{\pi}{4}+\frac{\pi}{12}\)
Step-by-step Solution
Detailed explanation
\(R = \sqrt{(\sqrt{3}-1)^2 + (\sqrt{3}+1)^2} = \sqrt{(4-2\sqrt{3}) + (4+2\sqrt{3})} = \sqrt{8} = 2\sqrt{2}\) \(\frac{\sqrt{3}-1}{2\sqrt{2}} \sin \theta + \frac{\sqrt{3}+1}{2\sqrt{2}} \cos \theta = \frac{2}{2\sqrt{2}}\)…
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