Question

The number of integral values of \( K \), for which the equation \( 7 \cos x + 5 \sin x = 2K + 1 \) has a solution, is

• A. 4
• B. 8
• C. 10
• D. 2

Hint:

For trigonometric equations, find the range of the expression and solve for the variable.

Answer 1

The Correct Option is B

Step 1: Solving for \( K \).
We solve the equation for \( K \) by equating it with the general form of a sinusoidal equation. The number of possible integral values of \( K \) is 8.

Step 2: Conclusion.
The correct number of integral values of \( K \) is 8, corresponding to option (2).