JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The number of solutions, of the equation \(\mathrm{e}^{\sin x}-2 e^{-\sin x}=2\) is
- A \(2\)
- B more than \(2\)
- C \(1\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
Take \(e^{\sin x}=t(t>0)\) \(\Rightarrow \mathrm{t}-\frac{2}{\mathrm{t}}=2\) \(\Rightarrow \frac{\mathrm{t}^2-2}{\mathrm{t}}=2\) \(\Rightarrow \mathrm{t}^2-2 \mathrm{t}-2=0\) \(\Rightarrow \mathrm{t}^2-2 \mathrm{t}+1=3\) \(\Rightarrow(\mathrm{t}-1)^2=3\)…
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