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

The general solution for cos(x)cos(2x)+sin(x)sin(2x)= 1/2 is x=-pi/3-2pin,x=-(5pi)/3-2pin

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

cos (x) cos (2 x) + sin (x) sin (2 x) = \frac{1}{2}

x = - \frac{π}{3} - 2 πn, x = - \frac{5 π}{3} - 2 πn

Solution steps

cos (x) cos (2 x) + sin (x) sin (2 x) = \frac{1}{2}

Rewrite using trig identities

cos (x - 2 x) = \frac{1}{2}

General solutions for

cos (x - 2 x) = \frac{1}{2}

x - 2 x = \frac{π}{3} + 2 πn, x - 2 x = \frac{5 π}{3} + 2 πn

Solve

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

Solve

x - 2 x = \frac{5 π}{3} + 2 πn : x = - \frac{5 π}{3} - 2 πn

x = - \frac{π}{3} - 2 πn, x = - \frac{5 π}{3} - 2 πn

2 csc^{2} (x) - 3 csc (x) - 2 = 0

csc (x) = \frac{2}{3}

8 - 7 cos (x) = 6 sin^{2} (x)

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

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

What is the general solution for cos(x)cos(2x)+sin(x)sin(2x)= 1/2 ?
The general solution for cos(x)cos(2x)+sin(x)sin(2x)= 1/2 is x=-pi/3-2pin,x=-(5pi)/3-2pin