What is the general solution for 2sin(3x)+2sin(x)=0 ?

The general solution for 2sin(3x)+2sin(x)=0 is x=2pin,x=pi+2pin,x=(3pi)/2+2pin,x= pi/2+2pin

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2sin(3x)+2sin(x)=0

2 sin (3 x) + 2 sin (x) = 0

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

2 sin (3 x) + 2 sin (x) = 0

Rewrite using trig identities

8 sin (x) - 8 sin^{3} (x) = 0

Solve by substitution

sin (x) = 0, sin (x) = - 1, sin (x) = 1

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

(cos (x) - 1) (3 cot (x) + 1) = 0

4 cot (x) = 3 csc (x)

x, sin (2 x) - cos (x) = 0

sin (θ) = \frac{7}{15}

tan^{2} (y) + 3 = 2 sec^{2} (y)

What is the general solution for 2sin(3x)+2sin(x)=0 ?
The general solution for 2sin(3x)+2sin(x)=0 is x=2pin,x=pi+2pin,x=(3pi)/2+2pin,x= pi/2+2pin