Question

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Answer 1

$2)Cos\alpha=\frac{x}{7}\\\\x=7*Cos\alpha=7*\frac{5}{7}=5\\\\S=\sqrt{7^{2}-5^{2}}=\sqrt{49-25}=\sqrt{24}=2\sqrt{6}\\\\Sin\alpha=\frac{2\sqrt{6}}{7}\\\\Ctg\alpha=\frac{5}{S}=\frac{5}{2\sqrt{6}}=\frac{5\sqrt{6}}{12}\\\\\\3)\frac{Ctg^{2}\alpha}{1+Ctg^{2}\alpha}*(1+tg^{2}\alpha) =\frac{\frac{Cos^{2}\alpha }{Sin^{2}\alpha}}{\frac{1}{Sin^{2}\alpha}}*\frac{1}{Cos^{2}\alpha} =\frac{Cos^{2} \alpha *Sin^{2}\alpha}{Sin^{2}\alpha*Cos^{2}\alpha}=1\\\\1=1-dokazano$