What is the general solution for sin(2x)+sin(6x)=2sin(4x) ?

The general solution for sin(2x)+sin(6x)=2sin(4x) is x=(pin)/2 ,x= pi/4+(pin)/2 ,x=pin

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sin(2x)+sin(6x)=2sin(4x)

sin (2 x) + sin (6 x) = 2 sin (4 x)

x = \frac{πn}{2}, x = \frac{π}{4} + \frac{πn}{2}, x = πn

Solution steps

sin (2 x) + sin (6 x) = 2 sin (4 x)

Subtract

2 sin (4 x)

from both sides

sin (2 x) + sin (6 x) - 2 sin (4 x) = 0

Rewrite using trig identities

- 2 sin (4 x) + 2 cos (2 x) sin (4 x) = 0

Factor

- 2 sin (4 x) + 2 cos (2 x) sin (4 x) : 2 sin (4 x) (cos (2 x) - 1)

2 sin (4 x) (cos (2 x) - 1) = 0

Solving each part separately

sin (4 x) = 0 or cos (2 x) - 1 = 0

sin (4 x) = 0 : x = \frac{πn}{2}, x = \frac{π}{4} + \frac{πn}{2}

cos (2 x) - 1 = 0 : x = πn

Combine all the solutions

x = \frac{πn}{2}, x = \frac{π}{4} + \frac{πn}{2}, x = πn

cos (x) = \frac{11}{2}

3 \frac{cos ^{2} ( a )}{sin ^{2} ( a )} = (cot (a))^{2}

cos (x) = \frac{- 2}{2}

tan (x) = - 0.22

θ, 1 + cos (θ) = 3 cos (θ)

What is the general solution for sin(2x)+sin(6x)=2sin(4x) ?
The general solution for sin(2x)+sin(6x)=2sin(4x) is x=(pin)/2 ,x= pi/4+(pin)/2 ,x=pin