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JEE Mains · Maths · STD 11 - Trigonometrical equations
Statement \(-1:\) The number of common solutions of the trigonometric equations \(2\,sin^2\,\theta - cos\,2\theta = 0\) and \(2 \,cos^2\,\theta - 3\,sin\,\theta = 0\) in the interval \([0, 2\pi ]\) is two. Statement \(-2:\) The number of solutions of the equation, \(2\,cos^2\,\theta - 3\,sin\,\theta = 0\) in the interval \([0, \pi ]\) is two.
- A Statement \(-1\) is true; Statement \(-2\) is true;Statement \(-2\) is a correct explanation for statement \(-1.\)
- B Statement \(-1\) is true; Statement \(-2\) is true;Statement \(-2\) is not a correct explanation for statement \(-1.\)
- C Statement \(-1\) is false; Statement \(-2\) is true.
- D Statement \(-1\) is true; Statement \(-2\) is false.
Answer & Solution
Correct Answer
(B) Statement \(-1\) is true; Statement \(-2\) is true;Statement \(-2\) is not a correct explanation for statement \(-1.\)
Step-by-step Solution
Detailed explanation
\(2\,{\sin ^2}\theta \, - \,\cos \,2\theta \, = \,0\) \( \Rightarrow \,2\,{\sin ^2}\theta \, - \,(1 - 2\,{\sin ^2}\theta )\, = \,0\) \( \Rightarrow \,2\,{\sin ^2}\theta \, - \,1 + 2\,{\sin ^2}\theta \, = \,0\)…
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