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

The general solution for sin(x)-sin(3x)=0 is x= pi/4+pin,x=(3pi)/4+pin,x=2pin,x=pi+2pin

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sin(x)-sin(3x)=0

sin (x) - sin (3 x) = 0

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = 2 πn, x = π + 2 πn

Solution steps

sin (x) - sin (3 x) = 0

Rewrite using trig identities

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

Solving each part separately

cos (2 x) = 0 or sin (x) = 0

cos (2 x) = 0 : x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = 2 πn, x = π + 2 πn

2 sin^{2} (θ) - 5 cos (θ) + 1 = 0

sec^{2} (x) cos (x) = cos (x), 0^{\circ} < x < 36 0^{\circ}

5 sin (x) - 4 = 2 cos (2 x)

csc (x) + cot (x) = 0

cos^{2} (θ) - sin^{2} (θ) = 0

What is the general solution for sin(x)-sin(3x)=0 ?
The general solution for sin(x)-sin(3x)=0 is x= pi/4+pin,x=(3pi)/4+pin,x=2pin,x=pi+2pin