Question

. If a = cos q + i sin q, find the value of 1 . 1

a

a​

Answer 1

Answer: ans.

Step-by-step explanation:

a=cosθ+isinθ

∴, 1+a/1-a

=(1+cosθ+isinθ)/(1-cosθ-isinθ)

=(1+cosθ+isinθ)(1-cosθ+isinθ)/(1-cosθ+isinθ)(1-cosθ-isinθ)

=(1+cosθ+isinθ-cosθ-cos²θ-isinθcosθ+isinθ+isinθcosθ+i²sin²θ)/{(1-cosθ)²-(isinθ)²}

=(1+2isinθ-cos²θ-sin²θ)/{1-2cosθ+cos²θ-(i²sin²θ)}

={1+2isinθ-(sin²θ+cos²θ)}/(1-2cosθ+cos²θ+sin²θ)

=(1+2isinθ-1)/(1-2cosθ+1)

=2isinθ/(2-2cosθ)

=isinθ/(1-cosθ)

=i(2sinθ/2cosθ/2)/(2sin²θ/2)

=(icosθ/2)/(sinθ/2)

=icotθ/2 Ans