### Questions (600)

 13 Prove that $\tan^{-1}\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}=\frac{\pi}{4}+\frac 12 \cos^{-1}x^2$ 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. 5 If $\tan A, \tan B, \tan C$ are roots of $x^3-ax^2+b=0$, find $(1+\tan^2 A)(1+\tan^2B)(1+\tan^2C)$ 5 Find $x$ in $4^x+6^x=9^x$ 4 If sum of the series $\frac {\tan 1}{\cos 2}+\frac{\tan 2}{\cos 4} +\frac{\tan 3}{\cos 6}...\frac{\tan 1024}{\cos 2048}=\tan \lambda -\tan \mu$

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 3 If $z=\frac{(\sqrt 3 - i)^{99}}{(1-i)^{101}}$, then the value of $\left(|z|\right)^{\frac{2}{97}}$ 0 In $\Delta ABC$, $\frac{b+c}{a}\le \csc A/2$, then $\csc^n A/2 \csc^n B/2 \csc^n C/2=2^{kn}$ for all integer $n\ge 1$, find $k$ 0 Complex inequality: find the max value. 0 A projectile motion problem with solution to be verified. 0 The set $(A \cap B^c)^c\cup (B\cap C)$ is equal to

### Tags (91)

 3 complex-numbers × 48 0 limits × 39 0 trigonometry × 84 0 sequences-and-series × 34 0 conic-sections × 75 0 quadratics × 30 0 calculus × 42 0 triangles × 29 0 functions × 41 0 kinematics × 28

### Bookmarks (19)

 19 Evaluating $\lim\limits_{n\to\infty} \sum_{k=1}^{n^2} \frac{n}{n^2+k^2}$ 18 Evaluate the limit $\lim\limits_{n \to \infty} \frac{1}{1+n^2} +\frac{2}{2+n^2}+ \ldots +\frac{n}{n+n^2}$ 4 Roots of a functionwith condition $\int_0^\pi f(x) \sin x dx = \int_0^\pi f(x) \cos x dx =0.$ 4 For any integer $n$, $a_n$ and $b_n$ are two real numbers and function....[CONT] 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 $g’’’(0)$