The number of elements in the set x [0,180^ ]: (x+100^ )= (x+50^ ) x (x-50^ ) is _ _ _ _ .

Step-by-step solution

(x+100°) x = (x+50°) (x-50°) (x+100°) x (x+100°) x = (x+50°) (x-50°) (x+50°) (x-50°) Applying Componendo & Dividendo: (2x+100°) 100° = 100° - 2x 2 (2x+100°) 2x + 200° = 0 (4x+100°) + 100° + 200° = 0 (4x+100°) = -2 150° 50° (4x+100°) = - 50° = (-40°) 4x + 100° = n + (-1)^n(-40°) x = n + (-1)^ n+1 (40°) - 100° 4 x = 30°, 55°, 120°, 145° in (0, ) Number of solutions = 4