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

The general solution for cos(θ)cos(2θ)+sin(θ)sin(2θ)=(sqrt(2))/2 is θ=-pi/4-2pin,θ=-(7pi)/4-2pin

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

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

θ = - \frac{π}{4} - 2 πn, θ = - \frac{7 π}{4} - 2 πn

Solution steps

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

Rewrite using trig identities

cos (θ - 2 θ) = \frac{2}{2}

General solutions for

cos (θ - 2 θ) = \frac{2}{2}

θ - 2 θ = \frac{π}{4} + 2 πn, θ - 2 θ = \frac{7 π}{4} + 2 πn

Solve

θ - 2 θ = \frac{π}{4} + 2 πn : θ = - \frac{π}{4} - 2 πn

Solve

θ - 2 θ = \frac{7 π}{4} + 2 πn : θ = - \frac{7 π}{4} - 2 πn

θ = - \frac{π}{4} - 2 πn, θ = - \frac{7 π}{4} - 2 πn

sec^{2} (x) - 2 tan (x) = 4

cos (4 x) = cos (2 x)

sin (4 x) + sin (2 x) = 0

10 sin (x) tan (x) - 9 tan (x) = 0

- sin (t) = 0

What is the general solution for cos(θ)cos(2θ)+sin(θ)sin(2θ)=(sqrt(2))/2 ?
The general solution for cos(θ)cos(2θ)+sin(θ)sin(2θ)=(sqrt(2))/2 is θ=-pi/4-2pin,θ=-(7pi)/4-2pin