Help me handwritten on white page just cooopyyy it in clear handwritten white page

Given, (sin x - 1)3 + (cos x - 1)3 + (sin x)3 = (2 sin x + COS X - 2)3 1 We know that, (a + b + c)3 = a3 + b3 + c3 + (a + b + c)(ab + bc + ca) Here a = sin x - 1, b = cos x - 1, c = sin x (a + b + c) = (2 sin x + cos x - 2) (ab + bc + ca) = (2 sin x + 2 sin x cos x - 3 sin x - COs X + 1) (1)(sin x - 1)3 + (cos x - 1)3 + (sin x)3 = (sin x - 1)3 + (cos x - 1)3 + (sin x)3 + (2 sin x + cos x - 2)(2 sin x + 2 sin x cos x - 3 sin x - cos x + 1) - (2 sin x + cos x - 2)(2 sin x + 2 sin x cos x - 2 sin x - sin x - cos x + 1) = 0 - (2 sin x + cos x - 2)(2 sin x - 1)(sin x + cos x - 1) = 0 (i) sin x = :. X= 6' 6 ( as x E [0, 27]) or (ii) sin x + cos x = 1 :. X = 0, 2 2n ( as x E [0, 27t]) or (iii) 2 sin x + cos x - 2 = 0 2(sin x - 1) = - COs X4 sin x - 8 sin x + 4 = cos2 x 5 sin2 x - 8 sin x + 3 = 0 .. sin x = 1 or Uil w cos x = 2(1 - sin x) 3 4 = 2(1 = sin x > 0 and cos x > 0 ... x has one solution in 1st quadrant. From (i), (ii),(iii), number of solutions of x = 6