Question

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задание на фотке

Answer 1

$\displaystyle\bf\\\frac{tgx+Ctgx}{(tg^{2} x+1)(Ctg^{2} x+1)} =\frac{\dfrac{Sinx}{Cosx} +\dfrac{Cosx}{Sinx} }{\dfrac{1}{Cos^{2} x} \cdot\dfrac{1}{Sin^{2} x} } =\\\\\\=\frac{\dfrac{Sin^{2}x+Cos^{2} x }{Sinx\cdot Cosx} }{\dfrac{1}{Sin^{2} x \cdot Cos^{2} x} } =\frac{1}{Sinx\cdot Cosx} \cdot Sin^{2} x Cos^{2}x =\\\\\\=Sinx Cosx=0,5\cdot 2Sinx Cosx=0,5Sin2x$