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Jan
6
revised Find the range of $k$ for which the inequality $k\cos^2x-k\cos x+1\geq0 ,\forall x\in(-\infty,\infty)$ holds.
added 188 characters in body
Jan
6
comment Find the range of $k$ for which the inequality $k\cos^2x-k\cos x+1\geq0 ,\forall x\in(-\infty,\infty)$ holds.
@Macavity Oh, how did I forget? That case was all that was running in my mind and I forgot to mention it. Editing in a second.
Jan
6
comment Find the range of $k$ for which the inequality $k\cos^2x-k\cos x+1\geq0 ,\forall x\in(-\infty,\infty)$ holds.
Please comment if I've missed out on anything.
Jan
6
answered Find the range of $k$ for which the inequality $k\cos^2x-k\cos x+1\geq0 ,\forall x\in(-\infty,\infty)$ holds.
Jan
4
comment The value of the polynomial at given point.
$x = \sqrt 2 - 1 \Rightarrow x + 1 = \sqrt{2} \Rightarrow (x+1)^2 = 2$ and so on. This technique was taught to me in my early days.
Jan
2
awarded  algebra-precalculus
Jan
1
comment The value of the polynomial at given point.
Here is the computation done by WolframAlpha, but you shouldn't have a problem doing it by hand.
Jan
1
answered The value of the polynomial at given point.
Nov
23
awarded  Nice Answer
Nov
8
comment prove polynomial division for any natural number
Do you know the properties of the complex cube roots of unity?
Oct
25
awarded  Good Answer
Oct
7
comment Which integers $a$, $b$ and $c$ satisfy the equation $a\sqrt{2} - b = c\sqrt{3}$?
(0, 0, 0) is the first answer that comes to mind.
Oct
7
answered Permutation in which the $A's$ appear together in a block of $4$ letters or the $B's$ appear together in a block of $3$ letters
Oct
7
comment Given that $x,y,z$ are positive reals such that $xyz=32$.What is the minimum value of $x^2+4xy+4y^2+2z^2$.
This was there in the VMC test yesterday, wasn't it?
Oct
1
awarded  Popular Question
Sep
29
comment Let $a\ne1$ be an nth root of identity, show $1+2a+3a^2+\dots + na^{n-1} = \frac{n}{a-1}$.
This technique is employed whenever you have an arithmetico-geometric series.
Sep
17
comment Proving $\sum_{n=0}^N n (n!) = (N+1)!-1$
Write $n\cdot n! = (n+1 - 1)\cdot n! = (n+1)! - n!$ and then it telescopes nicely. Standard technique.
Aug
7
answered Prove identity: $\frac{1+\sin\alpha-\cos\alpha}{1+\sin\alpha+\cos\alpha}=\tan\frac{\alpha}{2}$
Jun
24
awarded  Yearling
May
29
answered Find an acute angle $\gamma$ such that $\sin \gamma + \cos \gamma= \sqrt{2}$