Grade 12Trigonometry

sin2x+sin4x+sin6x=0 find genral solution of this question by alternative method

ashutosh

6 Years agoGrade 12

1 Answer

Vikas TU

6 Years ago

Dear student

sin²A + cos²A = 1
sin2A = 2sinAcosA
sin3A = -4sin³A + 3sinA

sin2x + sin4x + sin6x = 0 ==> siny + sin2y + sin3y = 0
siny + 2siny cosy - 4sin³y + 3siny = 0
2siny cosy - 4sin³y + 4siny = 0
siny cosy - 2sin³y + 2siny = 0
siny (cosy - 2sin²y + 2) = 0
siny (cosy - 2(1 - cos²y) + 2) = 0
siny (cosy - 2 + 2cos²y + 2) = 0
siny (cosy + 2cos²y) = 0
siny cosy (1 + 2cosy) = 0
2siny cosy (2cosy + 1) = 0
sin2y (2cosy + 1) = 0
sin2y = 0 OR cosy = -1/2
sin4x = 0 OR cos2x = -1/2

x = 0, π/4, π/3, π/2, 2π/3, 3π/4, π, 5π/4, 4π/3, 3π/2, 7π/4, 5π/3 ANSWER