What is the general solution for sin(3x)+sin(5x)=0 ?

The general solution for sin(3x)+sin(5x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin,x=(pin)/2 ,x= pi/4+(pin)/2

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sin(3x)+sin(5x)=0

sin (3 x) + sin (5 x) = 0

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

Solution steps

sin (3 x) + sin (5 x) = 0

Rewrite using trig identities

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

Solving each part separately

cos (x) = 0 or sin (4 x) = 0

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

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

Combine all the solutions

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

sec (x) = 1 - tan (x)

- cos (x) = cos (x)

2 cos (θ) - 1 = 0

6 sin^{2} (x) - 7 sin (x) + 2 = 0

5 sin (2 x) = 2 tan (3 0^{\circ})

What is the general solution for sin(3x)+sin(5x)=0 ?
The general solution for sin(3x)+sin(5x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin,x=(pin)/2 ,x= pi/4+(pin)/2