AP EAMCET · Maths · Trigonometric Equations
If \(2 \sin x-\cos 2 x=1\), then \(\left(3-2 \sin ^2 x\right)=\)
- A \(\sqrt{3}\)
- B \(-\sqrt{3}\)
- C \(\sqrt{5}\)
- D \(-\sqrt{5}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{5}\)
Step-by-step Solution
Detailed explanation
\(2 \sin x - (1 - 2\sin^2 x) = 1 \implies 2\sin^2 x + 2\sin x - 2 = 0 \implies \sin^2 x + \sin x - 1 = 0\) From \(\sin^2 x + \sin x - 1 = 0\), \(\sin x = \frac{-1 + \sqrt{1^2 - 4(1)(-1)}}{2} = \frac{-1 + \sqrt{5}}{2}\) (since \(-1 \le \sin x \le 1\))…
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