1. if a=cosθ+isinθ ,b=cosΦ+isinΦ ,c=cosψ+isinΨ and a⁄b+b/c+c/a=1 then cos(θ-Φ)+cos(Φ-ψ)+cos(ψ-θ) equals _________
2. if e^iθ =cosθ+isinθ then e^2micot-1p(pi+1/pi-1)equals

Dear Khushboo,

You can write a=e^θ, b=e^Φ, c=e^Ψ

Now a/b+b/c+c/a = e^θ-Φ+e^Φ-Ψ+e^Ψ-θ = 1 (given). Taking the real part of both the sides you get cos(θ-Φ)+cos(Φ-ψ)+cos(ψ-θ)=1

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Gokul  Joshi