[tex] \frac{(tgt+ctgt)sint}{tgt} = sin^{-1} t[/tex]. Created by Unbroken. algebra-ru

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[tex] \frac{(tgt+ctgt)sint}{tgt} = sin^{-1} t[/tex]

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NNNLLL54

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$\frac{(tgt+ctgt)\cdot sint}{tgt} = \frac{\left (\frac{sint}{cost}+\frac{cost}{sint}\right )\cdot sint}{\frac{sint}{cost}} =\frac{\frac{sin^2t+cos^2t}{sint\cdot cost}\cdot sint\cdot cost}{sint} =\\\\= \frac{1}{sint} =(sint)^{-1}$

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