Question

Ребята помогите алгебра
Скорей

Answer 1

$(\frac{1}{Sin\alpha}+\frac{1}{Cos\alpha})^{2}-(tg\alpha+\frac{1}{tg\alpha})^{2}=(\frac{Sin\alpha+Cos\alpha}{Sin\alpha Cos\alpha})^{2} -(\frac{Sin\alpha}{Cos\alpha}+\frac{Cos\alpha}{Sin\alpha})^{2}=\\\\=\frac{(Sin\alpha+Cos\alpha)^{2}}{Sin^{2}\alpha Cos^{2}\alpha }-(\frac{Sin^{2}\alpha+Cos^{2}\alpha}{Sin\alpha Cos\alpha})^{2}= \frac{(Sin\alpha+Cos\alpha)^{2}}{Sin^{2}\alpha Cos^{2}\alpha}-\frac{1}{Sin^{2} \alpha Cos^{2}\alpha}=$

$=\frac{Sin^{2}\alpha+2Sin\alpha Cos\alpha+Cos^{2}\alpha-1}{Sin^{2}\alpha Cos^{2}\alpha}=\frac{1+2Sin\alpha Cos\alpha-1}{Sin^{2}\alpha Cos^{2}\alpha} =\frac{2Sin\alpha Cos\alpha}{Sin^{2}\alpha Cos^{2}\alpha}=\frac{2}{Sin\alpha Cos\alpha}\\\\\frac{2}{Sin\alpha Cos\alpha}=\frac{2}{Sin\alpha Cos\alpha}$

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