Mathematics
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Aditya
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Score Newest
question
12
Prove that $\tan^{-1}\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}=\frac{\pi}{4}+\frac 12 \cos^{-1}x^2$
Jul 18, 2020
question
5
If $\tan A, \tan B, \tan C$ are roots of $x^3-ax^2+b=0$, find $(1+\tan^2 A)(1+\tan^2B)(1+\tan^2C)$
Apr 7, 2021
question
5
If $\omega$ is a cube root of unity $\not = 1$ then find the minimum value of $|a+b\omega +c\omega^2|$, where $a,b,c$ are integers but not all equal.
May 9, 2020
question
5
Find $x$ in $4^x+6^x=9^x$
Nov 16, 2019
question
4
Solve the given inequality below in the body.
Sep 4, 2019
question
4
If sum of the series $\frac {\tan 1}{\cos 2}+\frac{\tan 2}{\cos 4} +\frac{\tan 3}{\cos 6}...\frac{\tan 1024}{\cos 2048}=\tan \lambda -\tan \mu$
Dec 21, 2019
question
4
Let $f(x)=x+\frac{x^2}{2} + \frac{x^3}{3}+\frac{x^4}{4}+\frac{x^5}{5}$ and let $g(x)=f^{-1} (x)$. Find $g’’’(0)$
Aug 26, 2020
question
4
If $f(x):[1,3]\to [-1,1]$ satisfies $\int_1^3 f(x)dx=0$, then find max value of $\int_1^3 \frac{f(x)}{x}dx$
Jul 30, 2021
question
4
Let $f(x)$ be a polynomial satisfying $\lim_{x\to \infty} \frac {x^4 f(x)}{x^8+1} =3$, $f(2)=5$, $f(3)=10$,$f(-1)=2$,$f(-6)=37$. Find $f(0)$
Oct 11, 2020
question
4
For any integer $n$, $a_n$ and $b_n$ are two real numbers and function....[CONT]
Aug 10, 2020

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