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Author: Tinku Tara

if-x-1-x-1-3x-x-2-ax-2-bx-c-then-a-b-c-

Question Number 5507 by Kasih last updated on 17/May/16 $${if}\:\left({x}−\mathrm{1}\right)\:\left({x}+\mathrm{1}\right)\:+\mathrm{3}{x}+{x}^{\mathrm{2}} ={ax}^{\mathrm{2}} +{bx}+{c}\:{then}\:{a}=?\:{b}=?\:{c}=? \\ $$ Answered by Rasheed Soomro last updated on 17/May/16 $$\:\left({x}−\mathrm{1}\right)\:\left({x}+\mathrm{1}\right)\:+\mathrm{3}{x}+{x}^{\mathrm{2}} ={ax}^{\mathrm{2}} +{bx}+{c}…

if-the-degree-of-the-polynomial-p-x-is-less-than-the-degree-of-q-x-then-f-x-p-x-q-x-is-called-a-rational-function-

Question Number 5505 by Kasih last updated on 17/May/16 $${if}\:{the}\:{degree}\:{of}\:{the}\:{polynomial}\:{p}\left({x}\right)\:{is}\:{less}\:{than} \\ $$$${the}\:{degree}\:{of}\:{q}\left({x}\right)\:{then}\:{f}\left({x}\right)=\frac{{p}\left({x}\right)}{{q}\left({x}\right)}\:{is}\:{called}\:{a}\:.\:.\:.. \\ $$$${rational}\:{function} \\ $$$$ \\ $$ Commented by Rasheed Soomro last updated on…

nice-calculus-n-0-cos-n-x-cos-nx-solution-1-2-n-0-cos-n-1-x-cos-x-nx-cos-x-nx-2-n-0-cos-n-1-x-cos-n-1-x-

Question Number 136570 by mnjuly1970 last updated on 23/Mar/21 $$\:\:\:\:\:\:\:\:\:…….{nice}\:\:…..\:\:\:{calculus}….. \\ $$$$\:\:\:\:\Omega=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{cos}^{{n}} \left({x}\right).{cos}\left({nx}\right)=? \\ $$$$\:\:\:{solution}:::: \\ $$$$\:\:\:\:\Omega=\frac{\mathrm{1}}{\mathrm{2}}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{cos}^{{n}−\mathrm{1}} \left({x}\right)\left\{{cos}\left({x}−{nx}\right)+{cos}\left({x}+{nx}\right)\right. \\ $$$$\:\:\therefore\:\mathrm{2}\Omega=\underset{{n}=\mathrm{0}} {\overset{\infty}…

Why-does-cos-2-x-1-2-cos-2x-1-

Question Number 5495 by FilupSmith last updated on 16/May/16 $$\mathrm{Why}\:\mathrm{does}: \\ $$$$\mathrm{cos}^{\mathrm{2}} {x}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{cos}\left(\mathrm{2}{x}\right)+\mathrm{1}\right) \\ $$ Commented by Yozzii last updated on 16/May/16 $${Let}\:\boldsymbol{{a}}=\begin{pmatrix}{{cosA}}\\{{sinA}}\end{pmatrix}\:,\boldsymbol{{b}}=\begin{pmatrix}{{cosB}}\\{−{sinB}}\end{pmatrix}. \\ $$$${For}\:{all}\:\mathrm{0}<{A},{B}<\mathrm{2}\pi,\:{the}\:{angle}\:{between}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}\:{is}\:{A}+{B}…