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 6h comment Find all positive inegers solution for $x^2-xy-y^2=1$ $$4=(2x-y)^2-5y^2$$ 10h comment The angle giving minimum value 1d comment Prove that $\tan20^\circ\tan40^\circ\tan60^\circ\tan80^\circ=3$ 2d comment Prove: $\arcsin\left(\frac 35\right) - \arccos\left(\frac {12}{13}\right) = \arcsin\left(\frac {16}{65}\right)$ Apr 24 comment Let the smallest positive integer with six positive odd integer divisors and twelve positive even integer divisors, be n. What is the unit digit of n? artofproblemsolving.com/wiki/… Apr 24 comment Given that $\cos A + \cos B + \cos C = 0$ and $\sin A + \sin B + \sin C = 0$. @Ananya, Find the necessary & the sufficient condition : math.stackexchange.com/questions/1397066/… Apr 23 comment Is there a general rule to find period of multiplied functions? Provided $$\dfrac{p_1}{p_2}$$ is rational. In that the resultant period must divide the LCM Apr 23 comment Proving the GCD property of the Fibonacci numbers Apr 23 comment Solve the equation $\sqrt{1-x}=2x^2-1+2x\sqrt{1-x^2}$ @Ovi, So, the root is not $\cos126^\circ$ Apr 23 comment Solve the equation $\sqrt{1-x}=2x^2-1+2x\sqrt{1-x^2}$ Apr 23 comment Solve the equation $\sqrt{1-x}=2x^2-1+2x\sqrt{1-x^2}$ @астонвіллаолофмэллбэрг, If $x=\cos126^\circ,$ $$2x^2-1, x<0$$ The Right Hand Side $$=-\sqrt2\sin(45+72)^\circ=-\sqrt2\sin63^\circ$$ and the left $$=+\sqrt2\sin63^\circ$$ Apr 23 comment Prove that $\sin^2\frac{A}{2}\csc2A$, $\sin^2\frac{B}{2}\csc2B$, $\sin^2\frac{C}{2}\csc2C$ are in harmonic progression What is the source of the problem Apr 23 comment 100-th derivative of a function @Joel, Same as $$n=-1$$ right? Apr 23 comment Prove that $6(\sin^{10}A+\cos^{10}A) – 15(\sin^8A+\cos^8A) + 10(\sin^6A+\cos^6A) – 1 = 0​$ @HPDas, If $T_n=\cos^{2n}x+\sin^{2n}x$ $$T_0=2,T_1=1,T_{n+1}=T_n-\cos x\sin x\cdot T_{n-1}$$ To eliminate $\cos^2x,s=\sin^2x,$ $$6T_5-15T_4=-10T_3+1$$ Apr 22 comment Integral with irrational functions and polynomials Use partial fraction decomposition, $$\dfrac y{1-y^3}=\dfrac A{1-y}+\dfrac{By+C}{1+y+y^2}$$ $$\implies y=A(1+y+y^2)+(1-y)(By+C)$$ Or $y^3-1=(y-1)(y-\omega)(y-\omega^2)$ $y=1\implies3A=1$ Constant $\implies0=A+C\iff C=-A$ Coefficients of $x^2\implies 0=A-B\iff A=B$ Apr 22 comment Prove that $\tan^{-1}\frac{1}{3} + \tan^{-1}\frac{1}{7} + … + \tan^{-1}\frac{1}{n^2+n+1} = \tan^{-1}\frac{n}{n+2}$ Apr 22 comment Wolfram answer is different for the integral $\sqrt{\frac{x}{2-x}}dx$ @DavidH, Sorry for the typo Apr 21 comment Show whether this trigonometry series converges $$\le\dfrac{3n}{3^n}$$ Apr 21 comment Catalan numbers formula derivation Apr 21 comment 100-th derivative of a function @Stephan. The real part of $e^{i(n\pi/4+x)}$ is $\cos(n\pi/4+x)$ So, the real part of $2^{n/2}e^x\cdot e^{i(n\pi/4+x)}$ is $2^{n/2}e^x\cos(n\pi/4+x)$ which is the required answer