TS EAMCET · Maths · Trigonometric Equations
The general solution of the 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
Given, \((\sqrt{3}-1) \sin \theta+(\sqrt{3}+1) \cos \theta=2\) Let \(\quad \sqrt{3}-1=r \sin \alpha\) \(\ldots(i)\) and \(\quad \sqrt{3}+1=r \cos \alpha\) \(\therefore r^2\left(\sin ^2 \alpha+\cos ^2 \alpha\right)=(\sqrt{3}-1)^2+(\sqrt{3}+1)^2\)…
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