What is the modulus of the complex number (cos θ+i sin θ)/(cos θ-i sin θ) , where i=√(-1) ?

Question

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Correct answer: (B) 1. Z =(cos θ+i sin θ)/(cos θ-i sin θ) =((cos θ+i sin θ))/((cos θ-i sin θ)) × ((cos θ+i sin θ))/((cos θ+i sin θ)) =((cos θ+i sin θ)^2)/(cos^2 θ-(i sin θ)^2) =(cos 2 θ+i sin 2 θ)/(cos^2 θ+sin^2 θ)=cos 2 θ+i sin 2 θ Modulus of Z=|Z|=√(cos^2(2 θ)+sin^2(2 θ))=1

What is the modulus of the complex number $\frac{\cos \theta+i \sin \theta}{\cos \theta-i \sin \theta}$, where $i=\sqrt{-1}$ ?

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