TS EAMCET · Maths · Trigonometric Equations
The number of integral values of \(k\) for which the equation \(7 \cos x+5 \sin x=2 k+1\) has a solution, is
- A 4
- B 6
- C 8
- D 10
Answer & Solution
Correct Answer
(C) 8
Step-by-step Solution
Detailed explanation
We have, \[ 7 \cos x+5 \sin x=2 k+1 \] Maximum and minimum value of \(7 \cos x+5 \sin x\) is \(\sqrt{49+25},-\sqrt{49+25} \Rightarrow \sqrt{74},-\sqrt{74}\) \(\therefore-\sqrt{74} \leq 2 k+1 \leq \sqrt{74}\) \(\because k\) is an integer…
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