Category: Algebra

Question Number 207361 by hardmath last updated on 12/May/24 $$\mathrm{y}=\frac{\mathrm{tg}\mathbf{x}+\mathrm{ctg}\mathbf{x}}{8},(0;\frac{\pi }{2})$$$$\mathrm{Find}:\min \left(\mathrm{y}\right)=?$$ Answered by Berbere last updated on 12/May/24 $$ctg\left(x\right)=\frac{1}{y};y=tan\left(x\right)$$$$\Leftrightarrow{Min}\left(\frac{\mathrm{1}}{\mathrm{8}}\left({y}+\frac{\mathrm{1}}{{y}}\right);{y}\in\right]\mathrm{0},\infty\left[\right) \…

Question Number 207326 by hardmath last updated on 11/May/24 $$\mathrm{Find}:$$$$1.4{\cos }^{2}40°-\frac{1}{\cos 20°}=?$$$$2.4{\cos }^{2}40°+\frac{1}{\cos 20°}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 207315 by galva2000 last updated on 11/May/24 $$ifab+ac+bc=2$$$$calculateminimumof10a^2+10b^2+c^2$$ Answered by Berbere last updated on 11/May/24 $${S}=\mathrm{10}{a}^{\mathrm{2}} +\mathrm{10}{b}^{\mathrm{2}}…

Question Number 207330 by hardmath last updated on 11/May/24 $$\mathrm{Find}:4\cos 50°+\frac{1}{\sin 20°}=?$$ Answered by som(math1967) last updated on 12/May/24 $$\frac{4sin20cos50+1}{sin20}$$$$=\frac{2(sin70-sin30)+1}{sin20}$$$$=\frac{\mathrm{2}{sin}\mathrm{70}−\mathrm{1}+\mathrm{1}}{{cos}\left(\mathrm{90}−\mathrm{20}\right)} \…

Question Number 207226 by hardmath last updated on 10/May/24 $$\mathrm{Find}:\frac{{(2-\sqrt{2})}^8\cdot {(6+4\sqrt{2})}^8}{{(2+\sqrt{2})}^8}=?$$ Answered by Sutrisno last updated on 10/May/24 $${\left(\frac{(2-\sqrt{2})(6+4\sqrt{2})}{2+\sqrt{2}}\right)}^8$$$$\left(\frac{\left(\mathrm{2}−\sqrt{\mathrm{2}}\right)\left(\mathrm{6}+\mathrm{4}\sqrt{\mathrm{2}}\right)}{\mathrm{2}+\sqrt{\mathrm{2}}}.\frac{\mathrm{2}−\sqrt{\mathrm{2}}}{\mathrm{2}−\sqrt{\mathrm{2}}}\right)^{\mathrm{8}}…