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Category: Algebra

Question-199770

Question Number 199770 by Rupesh123 last updated on 09/Nov/23 Answered by aleks041103 last updated on 09/Nov/23 $${C}=\pi−\mathrm{3}\alpha \\ $$$$\Rightarrow\frac{\mathrm{5}}{{sin}\left(\mathrm{2}\alpha\right)}=\frac{\mathrm{6}}{{sin}\left(\pi−\mathrm{3}\alpha\right)}=\frac{\mathrm{6}}{{sin}\left(\mathrm{3}\alpha\right)} \\ $$$$\Rightarrow\mathrm{6}{sin}\left(\mathrm{2}\alpha\right)=\mathrm{5}{sin}\left(\mathrm{3}\alpha\right) \\ $$$${sin}\left(\mathrm{2}\alpha\right)=\mathrm{2}{sin}\left(\alpha\right){cos}\left(\alpha\right) \\ $$$${sin}\left(\mathrm{3}\alpha\right)={sin}\left(\mathrm{2}\alpha\right){cos}\left(\alpha\right)+{sin}\left(\alpha\right){cos}\left(\mathrm{2}\alpha\right)=…

Question-199732

Question Number 199732 by Rupesh123 last updated on 08/Nov/23 Answered by Rasheed.Sindhi last updated on 08/Nov/23 $${y}=\frac{{x}^{\mathrm{2}} +\mathrm{2}}{{x}+\mathrm{3}}=\frac{{x}^{\mathrm{2}} −\mathrm{9}+\mathrm{9}+\mathrm{2}}{{x}+\mathrm{3}} \\ $$$$\:\:\:=\frac{\left({x}−\mathrm{3}\right)\left({x}+\mathrm{3}\right)+\mathrm{11}}{{x}+\mathrm{3}} \\ $$$$=\left({x}−\mathrm{3}\right)+\frac{\mathrm{11}}{{x}+\mathrm{3}}\in\mathbb{Z}\Rightarrow\left({x}+\mathrm{3}\right)\mid\mathrm{11} \\ $$$${x}+\mathrm{3}=\pm\mathrm{1},\pm\mathrm{11}…