Category: Algebra

Question Number 65724 by bshahid010@gmail.com last updated on 02/Aug/19 Answered by mr W last updated on 03/Aug/19 $$S=\sin x+\cos x+\frac{1}{\sin x}+\frac{1}{\cos x}+\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}$$$$=\sin x+\cos x+\frac{\sin x+\cos x}{\sin x\cos x}+\frac{1}{\sin x\cos x}$$$$=\sin x+\cos x+\frac{\sin x+\cos x+1}{\sin x\cos x}$$$${let}\:\mathrm{sin}\:{x}+\mathrm{cos}\:{x}={t} \…

Question Number 65680 by bshahid010@gmail.com last updated on 01/Aug/19 Answered by mr W last updated on 02/Aug/19 Commented by mr W last updated on 02/Aug/19…

Question Number 131218 by shaker last updated on 02/Feb/21 Answered by mathmax by abdo last updated on 02/Feb/21 $$\mathrm{I}\:=\int_{−\mathrm{2}} ^{\mathrm{2}} \:\frac{\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }}{\mathrm{4}^{\mathrm{x}} \:+\mathrm{1}}\:\Rightarrow\mathrm{I}\:=_{\mathrm{x}=−\mathrm{t}} \:\:\:\int_{−\mathrm{2}} ^{\mathrm{2}}…

Question Number 131201 by shaker last updated on 02/Feb/21 Answered by liberty last updated on 11/Feb/21 $$\mathrm{L}=\int \frac{\tan {}^2\mathrm{x}}{\cos 2\mathrm{x}}\mathrm{dx};\mathrm{by}\mathrm{change}\mathrm{of}\mathrm{variable}$$$$\mathrm{let}\mathrm{u}=\tan \mathrm{x}\to \{\begin{array}{l}\mathrm{dx}=\frac{\mathrm{du}}{1+{\mathrm{u}}^2}\\ \cos 2\mathrm{x}=\frac{1-{\mathrm{u}}^2}{1+{\mathrm{u}}^2}\end{array}$$$$\mathrm{L}=\int\:\left(\frac{\mathrm{u}^{\mathrm{2}}…

Question Number 96 by sudhanshur last updated on 25/Jan/15 $$x={17}^4\mathrm{and}y=14\times 16\times 18\times 20\mathrm{then}$$$$\mathrm{which}\mathrm{is}\mathrm{greater}?$$ Answered by anoopsingh7374@gmail.com last updated on 27/Nov/14 $$$$…