AP EAMCET · Maths · Trigonometric Equations
If \(k \in R\) is such that the equation \(2 \cosh ^2 x=3 \sinh x+k\) has no real solution, then which of the following is correct?
- A \(k < \frac{1}{2}\)
- B \(k < \frac{3}{8}\)
- C \(k < \frac{7}{8}\)
- D \(k < \frac{5}{8}\)
Answer & Solution
Correct Answer
(C) \(k < \frac{7}{8}\)
Step-by-step Solution
Detailed explanation
Given, \(2 \cosh ^2 x-3 \sinh x-k=0\) has no real solution. \(\because \quad \cosh ^2 x-\sinh ^2 x=1\) \(\Rightarrow \quad \cosh ^2 x=1+\sinh ^2 x\) Then, \(2\left(1+\sinh ^2 x\right)-3 \sinh x-k=0\) \(\Rightarrow \quad 2 \sinh ^2 x-3 \sinh x+(2-k)=0\) Above equation has no real…
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