What is the general solution for cos(θ)cos(2θ)+sin(θ)sin(2θ)=(sqrt(3))/2 ?

The general solution for cos(θ)cos(2θ)+sin(θ)sin(2θ)=(sqrt(3))/2 is θ=-pi/6-2pin,θ=-(11pi)/6-2pin

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cos(θ)cos(2θ)+sin(θ)sin(2θ)=(sqrt(3))/2

cos (θ) cos (2 θ) + sin (θ) sin (2 θ) = \frac{3}{2}

θ = - \frac{π}{6} - 2 πn, θ = - \frac{11 π}{6} - 2 πn

Solution steps

cos (θ) cos (2 θ) + sin (θ) sin (2 θ) = \frac{3}{2}

Rewrite using trig identities

cos (θ - 2 θ) = \frac{3}{2}

General solutions for

cos (θ - 2 θ) = \frac{3}{2}

θ - 2 θ = \frac{π}{6} + 2 πn, θ - 2 θ = \frac{11 π}{6} + 2 πn

Solve

θ - 2 θ = \frac{π}{6} + 2 πn : θ = - \frac{π}{6} - 2 πn

Solve

θ - 2 θ = \frac{11 π}{6} + 2 πn : θ = - \frac{11 π}{6} - 2 πn

θ = - \frac{π}{6} - 2 πn, θ = - \frac{11 π}{6} - 2 πn

3 cos (2 x) - 2 cos (x) - 1 = 0

sin (3 π x) = 0

tan (2 t) = 1, 0 \leq t < 2 π

sin^{2} (x) = cot (x)

sin (\frac{x}{2}) = 1, 0 \leq x < 2 π

What is the general solution for cos(θ)cos(2θ)+sin(θ)sin(2θ)=(sqrt(3))/2 ?
The general solution for cos(θ)cos(2θ)+sin(θ)sin(2θ)=(sqrt(3))/2 is θ=-pi/6-2pin,θ=-(11pi)/6-2pin