Find the general solution for cos2θ=(√2+1)(cosθ-1/√2)

Steps to solve find the general solution for cos2θ=(√2+1)(cosθ-1/√2)

⇒cos2θ=(√2+1)(cosθ-1/√2)

⇒2cos^2θ-1=(√2+1)cosθ-(√2+1)/√2

⇒2cos^2θ-(√2+1)cosθ+(√2+1)/√2-1=0

⇒2cos^2θ-(√2+1)cosθ+(√2+1-√2)/√2=0

⇒2cos^2θ-(√2+1)cosθ+1/√2=0

Here a=2, b=√2+1, c=1/√2

cosθ={-b±√(b^2-4ac)}/2a={(√2+1)±(√2-1)}/4

⇒cosθ={(√2+1)+(√2-1)}/4 OR cosθ={(√2+1)-(√2-1)}/4

⇒cosθ=2√2/4 OR cosθ=1/2

⇒cosθ=1/√2 OR cosθ=1/2

⇒θ=π/4 OR θ=π/3

⇒θ=2nπ±π/θ OR ⇒θ=2nπ±π/3

Hence the general solutions for cos2θ=(√2+1)(cosθ-1/√2) are θ=2nπ±π/θ OR θ=2nπ±π/3

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