What is the general solution for sin(2x)cos(x)+cos(2x)sin(x)=1 ?

The general solution for sin(2x)cos(x)+cos(2x)sin(x)=1 is x= pi/6+(2pin)/3

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

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

x = \frac{π}{6} + \frac{2 πn}{3}

Solution steps

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

Rewrite using trig identities

sin (2 x + x) = 1

General solutions for

sin (2 x + x) = 1

2 x + x = \frac{π}{2} + 2 πn

Solve

2 x + x = \frac{π}{2} + 2 πn : x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

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

- 10 sin (θ) + 2 = 2

cot (u) - csc (u) = \frac{sin ( u )}{1 + cos ( u )}

sin (x) = \frac{5}{3}

sin (θ) = \frac{3}{4}

What is the general solution for sin(2x)cos(x)+cos(2x)sin(x)=1 ?
The general solution for sin(2x)cos(x)+cos(2x)sin(x)=1 is x= pi/6+(2pin)/3