WBJEE · Maths · Limits
\(\cos (2 x+7)=a(2-\sin x)\) can have a real solution for
- A all real values of a
- B \(a \in[2,6]\)
- C \(\mathrm{a} \in[-\infty, 2] \backslash\{0\}\)
- D \(\mathrm{a} \in(0, \infty)\)
Answer & Solution
Correct Answer
(B) \(a \in[2,6]\)
Step-by-step Solution
Detailed explanation
Step 1. find the solution of given equation: \(\begin{aligned} &\cos 2 x+a \sin x=2 a-7 \\ &\Rightarrow 1-2 \sin ^2 x+a \sin x=2 a-7 ;\left[\because \cos 2 x=1-2 \sin ^2 x\right] \\ &\Rightarrow 2 \sin ^2 x-a \sin x+2 a-8=0 \end{aligned}\) Step 2. Find the roots of above…
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