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If, $a=\cos \alpha+i \sin \alpha, b=\cos \beta+i \sin \beta$ and $c=\cos \gamma+i \sin \gamma$ find the value of, $\frac{a b}{c}-\frac{c}{a b}$.
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written 2.1 years ago by
prajapatijaimin
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• modified 2.1 years ago |
Solution:
Given:
$ \begin{aligned} a &=\cos \alpha+i \sin \alpha \\\\ b &=\cos \beta+i \sin \beta \\\\ \& c & =\cos \gamma+i \sin \gamma \end{aligned}\\ $
Now,
$ \frac{\mathrm{ab}}{\mathrm{c}}=\mathrm{ab}(\mathrm{c})^{-1}\\ $
$ =(\cos \alpha+i \sin \alpha)(\cos \beta+i \sin \beta)(\cos \gamma+i \sin \gamma)^{-1}\\ $
$ =(\cos \alpha+i \sin \alpha)(\cos \beta+i \sin \beta)(\cos \gamma-i …
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