Category: Algebra

Question Number 188286 by mustafazaheen last updated on 27/Feb/23 $$whensin\left(x\right)+cos\left(x\right)=a$$$$findsec\left(x\right)+csc\left(x\right)=?$$ Answered by ARUNG_Brandon_MBU last updated on 27/Feb/23 $$\sin x+\cos x=a\Rightarrow \sin x\cos x=\frac{a^2-1}{2}$$$$\mathrm{sec}{x}+\mathrm{cosec}{x}=\frac{\mathrm{sin}{x}+\mathrm{cos}{x}}{\mathrm{sin}{x}\mathrm{cos}{x}}=\frac{\mathrm{2}{a}}{{a}^{\mathrm{2}}…

Question Number 188270 by mnjuly1970 last updated on 27/Feb/23 Commented by mnjuly1970 last updated on 27/Feb/23 $$inA\stackrel{\mathrm{\Delta }}{BC}prove:$$$$\frac{1}{cos\left(A\right)}+\frac{1}{cos\left(B\right)}+\frac{1}{cos\left(C\right)}⩾6$$$$$$$$\:\:\:\:\:{note}\::\:\mathrm{0}\:<\:{A}\:,\:{B}\:,\:{C}\:<\:\mathrm{90}^{°} \…

Question Number 188262 by normans last updated on 27/Feb/23 $$$$$$\mathit{s}\mathit{o}\mathit{l}\mathit{v}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{e}\mathit{q}\mathit{u}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n};$$$$\begin{array}{c}\mathit{x}+\mathit{y}+\mathit{z}=30\sqrt{2}\\ \mathit{x}-\mathit{y}-\mathit{z}=7,5\\ \mathit{x}+\mathit{y}-\mathit{z}=\sqrt{22}\end{array}\}$$$$\mathit{x};\mathit{y};\mathit{z}=??$$$$$$$$theyformfunnypositions$$$$$$ Answered…

Question Number 188247 by cortano12 last updated on 27/Feb/23 $$\mathrm{Prove}\mathrm{that}$$$$\left(1\right){5555}^{2222}+{2222}^{5555}\mathrm{divisible}\mathrm{by}7$$$$\left(2\right)3^{105}+4^{105}\mathrm{divisible}\mathrm{by}7$$ Answered by Rasheed.Sindhi last updated…

Question Number 188224 by Shrinava last updated on 26/Feb/23 $$\mathrm{If}\mathrm{\Omega }=\underset{\mathbf{n}=1}{\sum ^{\mathrm{\infty }}}{\left(\underset{\mathbf{k}=2}{\prod ^{\mathrm{\infty }}}\frac{{\mathrm{k}}^3-1}{{\mathrm{k}}^3+1}\right)}^{\mathbf{n}}$$$$\mathrm{Solve}\mathrm{for}\mathrm{complex}\mathrm{numbees}:$$$${\mathrm{z}}^4+{3\mathrm{z}}^3+\mathrm{\Omega }{\mathrm{z}}^2+3\mathrm{z}+1=0$$…