Question

Solution of sinx + sin5x = sin 3x in (0,ℼ/2) are..?

Answer 1

Given the equation sin(x) + sin(5x) = sin(3x): This can be simplified as follows:

2 sin(3x) cos(2x) = sin(3x) This implies: sin(3x) (2 cos(2x) - 1) = 0

Therefore, the equation is satisfied when sin(3x) = 0 or when 2 cos(2x) - 1 = 0.

To find the solutions: For sin(3x) = 0, we have 3x = π (or any integer multiple of π). For 2 cos(2x) - 1 = 0, we have 2x = π/3.

Thus, the possible solutions are x = 0, x = π/3, or x = π/6.

Hence, the solutions to the equation sin(x) + sin(5x) = sin(3x) are π/3 and π/6.