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If, a=cosα+isinα,b=cosβ+isinβ and c=cosγ+isinγ find the value of, abc−cab.
1 Answer
written 3.0 years ago by | • modified 3.0 years ago |
Solution:
Given:
a=cosα+isinαb=cosβ+isinβ&c=cosγ+isinγ
Now,
abc=ab(c)−1
=(cosα+isinα)(cosβ+isinβ)(cosγ+isinγ)−1
=(cosα+isinα)(cosβ+isinβ)(cosγ−isinγ)
⇒abc=cos(α+β−γ)+isin(α+β−γ)
also,cab=[[abc]−1]
=[cos(α+β−γ)+isin(α+β−γ)]−1
⇒cab=cos(α+β−γ)−isin(α+β−γ)
∴(1)−(2) then,
abc−cab=cos(α+β−γ)+isin(α+β−γ)−cos(α+β−γ)+isin(α+β−γ) ⇒abc−cab=2isin(α+β−γ)