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

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

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

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

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

Solution steps

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

Rewrite using trig identities

sin (x + 2 x) = 0

General solutions for

sin (x + 2 x) = 0

x + 2 x = 0 + 2 πn, x + 2 x = π + 2 πn

Solve

x + 2 x = 0 + 2 πn : x = \frac{2 πn}{3}

Solve

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

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

7 cos (5 x) + 9 = 12

cos (2 x) + 1 = sin (2 x)

3 cot (2 x) = - 1

sin^{2} (x) - 1 = cos^{2} (x)

cos (θ) = 3

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