Question

solve sin4x+sin3x+sin2x=0​

Answer 1

Answer:

To solve for x from the given trigonometric equation. There could be multiple solutions too.

x =  0, n * π , 60° , 120°, 240° , 300°

Step-by-step explanation:

Sin 4x  + Sin 3x  + Sin 2 x = 0

Sin 2x = 2 Sin x * Cos x

Sin 3x = 3 sin x  - 4 sin³ x

Sin 4 x = 2 Sin 2x * Cos 2x

Sin 4x + Sin 2x = 2 Sin (4x + 2x)/2  * Cos (4x - 2x)/2

                         = 2 Sin 3x * Cos x

So LHS = 2 Sin 3x * Cos x + Sin 3x  = 0

            = Sin 3x * (2 Cos x + 1) = 0

So either sin 3x = 0,    or   Cos x = -1/2,  ie.,   x =  2π/3,

Sin 3x =  3 Sin x - 4 Sin³ x = 0  means

   Sin x * (3 - 4 Sin² x) = 0

=> Sin x = 0  ie.,   x = 0, or π  or 2 π or n * π, where n is an integer.

   Also it can be that  3 = 4 Sin² x

So Sin x =  ± √3/2   means that  x = π/3, 2π/3, 2π - π/3 etc.