a.maths question

Using formula
sin A - sin B = 2cos[(A + B)/2]sin[(A - B)/2]
cosA – cosB = - 2sin[(A + B)/2]sin[(A - B)/2]
cos(A+B) = cosAcosB - sinAsinB
SOLUTION
sin3x+cos3x=sin2x+cos2x
sin3x – sin2x + cos3x – cos2x = 0
2cos[(3x + 2x)/2]sin[(3x – 2x)/2] + 2sin[(3x + 2x)/2]sin[(3x – 2x)/2] = 0
2cos(2.5x)sin(0.5x) - 2sin(2.5x)sin(0.5x) = 0
2[cos(2.5x) – sin(2.5x)]sin(0.5x) = 0 [divided by cos(2.5x)]
2[1 – tan(2.5x)]sin(0.5x) = 0
sin 0.5x = 0 or tan(2.5x) = 1
when sin(0.5x) = 0
0.5x = 0 or 0.5x = 180
So x = 0 or or = 360
when tan(2.5x) = 1
2.5x = 45 or 2.5x = 225 or 2.5x = 405 or 2.5x = 585 or 2.5x = 765
x = 18 or x = 90 or x = 162 or x = 234 or x = 306

Using formula

sin A - sin B = 2cos[(A + B)/2]sin[(A - B)/2]

cosA – cosB = - 2sin[(A + B)/2]sin[(A - B)/2]

cos(A+B) = cosAcosB - sinAsinB

SOLUTION

sin3x+cos3x=sin2x+cos2x

sin3x – sin2x + cos3x – cos2x = 0

2cos[(3x + 2x)/2]sin[(3x – 2x)/2] + 2sin[(3x + 2x)/2]sin[(3x – 2x)/2] = 0

2cos(2.5x)sin(0.5x) - 2sin(2.5x)sin(0.5x) = 0

2[cos(2.5x) – sin(2.5x)]sin(0.5x) = 0 [divided by cos(2.5x)]

2[1 – tan(2.5x)]sin(0.5x) = 0

sin 0.5x = 0 or tan(2.5x) = 1

when sin(0.5x) = 0

0.5x = 0 or 0.5x = 180

So x = 0 or or = 360

when tan(2.5x) = 1

2.5x = 45 or 2.5x = 225 or 2.5x = 405 or 2.5x = 585 or 2.5x = 765

x = 18 or x = 90 or x = 162 or x = 234 or x = 306