JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
The number of integral values of \('k'\) for which the equation \(3 \sin x+4 \cos x=k+1\) has a solution, \(k\) \(\in R\) is
- A \(11\)
- B \(22\)
- C \(33\)
- D \(7\)
Answer & Solution
Correct Answer
(A) \(11\)
Step-by-step Solution
Detailed explanation
\(3 \sin x+4 \cos x=k+1\) \(\Rightarrow k +1 \in\left[-\sqrt{3^{2}+4^{2}}, \sqrt{3^{2}+4^{2}}\right]\) \(\Rightarrow k +1 \in[-5,5]\) \(\Rightarrow k \in[-6,4]\) No. of integral values of \(k =11\)
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