Question

Number of solutions of the equation sin 9θ=sinθ in the interval [0,2π] is:

• A. 16
• B. 17
• C. 18
• D. 15

Hint:

Always count overlaps carefully when solving sin A=sin B.

Answer 1

The Correct Option is C

Step 1: sin A=sin B ⟹ A=B+2kπ or A=π-B+2kπ.
Step 2: So, 9θ=θ+2kπ ⟹ θ=(kπ)/(4) and 9θ=π-θ+2kπ ⟹ θ=((2k+1)π)/(10).
Step 3: Counting distinct solutions in [0,2π] gives 18.