(tgt-sint*cost)=2ctg^2t...

Ilyas0508 @Ilyas0508

July 2022 1 1 Report

Докажите тождество.
((sint+cost)^2-1)/(tgt-sint*cost)=2ctg^2t

Answers & Comments

red321 Преобразуем левую часть.
$\frac{(sint+cost)^2-1}{tgt-sint*cost}=\frac{sin^2t+cos^2t+2sintcost-1}{\frac{sint}{cost}-sint*cost}=\frac{1+2sintcost-1}{sint(\frac{1}{cost}-cost)}=\frac{2cost}{\frac{1-cos^2t}{cost}}=\\=\frac{2cos^2t}{sin^2t}=2ctg^2t$

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