Use sum-to-product formulas to find the solutions of the equation. (Use n as your arbitrary integer. Enter your answers as a comma-separated list.)

Question

Use sum-to-product formulas to find the solutions of the equation. (Use n as your arbitrary integer. Enter your answers as a comma-separated list.)

(A). sin 13t + sin 11t = 0

(B). cos 6x + cos 8x = cos x

Answer 1

(A) sin13t + sin11t = 0; 2sin12tcost = 0;

sin12t = 0. 12t = πn, t = πn/12;

cost = 0, t = π/2 + πn

where n = 0,±1, ±2, ...

(B) cos6x + cos8x = cosx;

2cos7xcosx - cosx = 0; cosx(2cos7x - 1) = 0.

cosx = 0, x = π/2 + πn,

2cos7x - 1 = 0; cos7x = 1/2; 7x = π/3 + 2πn or 7x = 5π/3 + 2πn

x = π/21 + 2πn/7 or x = 5π/21 + 2πn/7

n = 0,±1, ±2, ...