Find the general solution for secθ-1=(√2-1)tanθ

Steps to solve Find the general solution for secθ-1=(√2-1)tanθ

⇒secθ-1=(√2-1)tanθ

⇒(1/cosθ)-1=(√2-1)sinθ/cosθ

⇒(1-cosθ)/cosθ=(√2-1)sinθ/cosθ

⇒(1-cosθ)=(√2-1)sinθ

⇒2sin^2(θ/2)=(√2-1)2sin(θ/2).cos(θ/2)

⇒2sin^2(θ/2)-(√2-1)2sin(θ/2).cos(θ/2)=0

⇒2sin(θ/2){sin(θ/2)-(√2-1).cos(θ/2)}=0

⇒2sin(θ/2)=0 OR sin(θ/2)-(√2-1).cos(θ/2)=0{Impossible}

⇒sin(θ/2)=0

⇒θ/2=0

⇒θ=2nπ

Hence the general solution for secθ-1=(√2-1)tanθ is 2nπ

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