Question

The equation \(3\cos x + 4\sin x = 6\) has ... solution.

• A. finite
• B. infinite
• C. one
• D. no

Hint:

\(a\cos x + b\sin x\) lies between \(-\sqrt{a^2 + b^2}\) and \(\sqrt{a^2 + b^2}\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Maximum value of \(a\cos x + b\sin x\) is \(\sqrt{a^2 + b^2}\).
Step 2: Detailed Explanation:
Max of \(3\cos x + 4\sin x = \sqrt{9 + 16} = 5\)
Given equation equals \(6>5\), so no solution.
Step 3: Final Answer:
No solution.