Solve the equation 2sinxcosx cosx 0 csc2x 2cot2x 0Soluti

Solve the equation

2sin(x)cos(x) + cos(x) = 0

csc²x – 2cot²x = 0

Solution

1) 2sin(x)cos(x) + cos(x) = 0

cos(x)*[2sin x + 1] = 0

cos x = 0 =========> x = 90, 270 degree

and [2sin x + 1] = 0 =====> sin x = -1/2 ====> x = 210, 330 degree

2) csc2x – 2cot2x = 0

1/sin2x - 2cos2x/sin2x = 0

(1 - 2cos2x)/sin2x = 0

1 - 2cos2x = 0 ==========> cos2x = 1/2

x = 30, 150 degree