Solve these equations sin x pi4 sinx pi4 1 Apply the sum

Solve these equations: sin (x + pi/4) - sin(x - pi/4) = 1 Apply the sum and difference formulas for sine to simplify the left-hand Side of the equation. Find all solutions to the equation you found in part I.

Solution

LHS = sin(x+/4)-sin(x-/4) = (sinx cos /4 +cosx sin/4) - (sinx cos/4 - cosx sin/4) = 2 cosx sin/4

Therefore,

2 cosx (1/2) = 1

=> cosx = 1/2

=> x = 2n + /4 or 2n - /4