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/2+(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}{2} + \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{3 π}{2} + 2 πn

Solve

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

x = \frac{π}{2} + \frac{2 πn}{3}

2 cos (x) = 0.2

cos (a) = - sin (a)

\frac{8}{sin ( 4 5 ^{\circ} )} = \frac{42}{sin ( x )}

sin (x) cos (x) = 3

- 2 cos^{2} (4 x) + 2 sin (4 x) - 1 = 0

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/2+(2pin)/3