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TS EAMCET · Maths · Trigonometric Equations

If \(\left|\sin x-\cos ^2 x\right| \geq\left|3-3 \sin x+\sin ^2 x\right|+4|\sin x-1|\), then \(x=\)

  1. A \((4 n+1) \frac{\pi}{2}, n \in Z\)
  2. B \(2 n \pi+\frac{\pi}{3}, n \in Z\)
  3. C \(n \pi+\frac{\pi}{2}, n \in Z\)
  4. D \(2 n \pi+\frac{\pi}{6}, n \in Z\)
Verified Solution

Answer & Solution

Correct Answer

(A) \((4 n+1) \frac{\pi}{2}, n \in Z\)

Step-by-step Solution

Detailed explanation

It is given that, \(\left|\sin x-\cos ^2 x\right| \geq\left|3-3 \sin x+\sin ^2 x\right|+4|\sin x-1|\) \(\Rightarrow\left|\sin ^2 x+\sin x-1\right| \geq\left|\sin ^2 x-3 \sin x+3\right|\) \(+|4 \sin x-4|\) \(\Rightarrow\left|\left(\sin ^2 x-3 \sin x+3\right)+(4 \sin x-4)\right|\)…