Solve sin2xcos3x cos2xsin3x 1 There should be 5 solutions

Solve sin(2x)cos(3x) + cos(2x)sin(3x) = -1 There should be 5 solutions total

sin(2x)cos(3x) + cos(2x)sin(3x) = -1

use the formula : sin(x+y) = sinxcosy +cosxsiny

So, sin(2x)cos(3x) + cos(2x)sin(3x) = sin(2x +3x)

sin5x = -1

5x = sin^-1(-1)

5x = 3pi/2

general solution : x = 3pi/10 +2k*pi/5

k =0 ; x= 3pi/10

k =1 \' x= 3pi/10 +2pi/5 = 7pi/10

k = 2; x= 11pi/10

k = 3; x= 15pi/10

k =4 ; x= 19pi/10

Solution : five values of x = 3pi/10 ,7pi/10 , 11pi/10 , 15pi/10 , 19pi/10