Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
cos(x+3pi/4) - cos(x-3pi/4) = 1
2 answers
right
cos(x+3pi/4) = cosx cos(3π/4) - sinx sin(3π/4)
cos(x - (3π/4)) = cosx cos(3π/4) + sinx sin(3π/4)
cos(x+3pi/4) - cos(x-3pi/4) = 1
cosx cos(3π/4) - sinx sin(3π/4) - cosx cos(3π/4) - sinx sin(3π/4) = 1
-2sinx sin(3π/4) = 1
sinx (√2/2) = -1/2
sinx = (-1/2)(2/√2) = -1/√2
x = 225° or x = 315°
x = 5π/4 or x = 7π/4
cos(x - (3π/4)) = cosx cos(3π/4) + sinx sin(3π/4)
cos(x+3pi/4) - cos(x-3pi/4) = 1
cosx cos(3π/4) - sinx sin(3π/4) - cosx cos(3π/4) - sinx sin(3π/4) = 1
-2sinx sin(3π/4) = 1
sinx (√2/2) = -1/2
sinx = (-1/2)(2/√2) = -1/√2
x = 225° or x = 315°
x = 5π/4 or x = 7π/4
1 answer