JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
Let \(S = \{x \in [-\pi, \pi] : \sin x (\sin x + \cos x) = a, a \in \mathbb{Z}\}\). Then \(n(S)\) is equal to :
- A \(3\)
- B \(6\)
- C \(7\)
- D \(9\)
Answer & Solution
Correct Answer
(D) \(9\)
Step-by-step Solution
Detailed explanation
Given the equation: \(\sin x (\sin x + \cos x) = a\) \(\Rightarrow \sin^2 x + \sin x \cos x = a\) Using the double angle formulas \(\sin^2 x = \dfrac{1 - \cos 2x}{2}\) and \(\sin x \cos x = \dfrac{\sin 2x}{2}\), we get: \(\dfrac{1 - \cos 2x}{2} + \dfrac{\sin 2x}{2} = a\)…
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