Question

sin 3X= sin 2X find the general solution​

Answer 1

Answer:

Hey mate here is your answer

Step-by-step explanation:

sin3x = sin2x

sin3x - sin2x = 0

but sin(A+B) - sin(A-B) = 2sinBcosA

A + B = 3x; -A + B = -2x

2A = 5x ; A = 5x/2

2B = x; B = x/2

Therefore sin(3x) - sin(2x) = 2sin(x/2)cos(5x/2) = 0

i.e.:

sin(x/2) = 0

x/2 = n(pi); x = 2n(pi) (n = 0, +/-1, +/-2,....)

OR cos(5x/2) = 0

(+/-)5x/2 = n(pi)/2

i.e. 5x/2 = n(pi/2) OR 5x/2 = -n(pi/2)

x = n(pi)/5 or x = -n(pi)/5

therefore x = +/- (n)(pi)/5

but n already includes the +/-;

therefore x = npi/5

Therefore, x = n(pi)/5 or x = 2npi

but n(pi)/5 includes 2n(pi)

therefore general solution: x = n(pi)/5

hope this helps you