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pi-π
  • Member for 5 years, 11 months
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9 votes
4 answers
2k views

A spherical ball of salt is dissolving in water

8 votes
1 answer
874 views

Help with this trigonometry problem

8 votes
6 answers
9k views

The sum of digits in a 2-digit number

8 votes
2 answers
2k views

Prove: If $x+y+z=xyz$ then $\frac {x}{1-x^2} +\frac {y}{1-y^2} + \frac {z}{1-z^2}=\frac {4xyz}{(1-x^2)(1-y^2)(1-z^2)}$

7 votes
8 answers
8k views

Prove: $\cos^3{A} + \cos^3{(120°+A)} + \cos^3{(240°+A)}=\frac {3}{4} \cos{3A}$

7 votes
3 answers
2k views

Integrate $\int \frac {\sin (2x)}{(\sin x+\cos x)^2}\,dx$

6 votes
2 answers
269 views

Consider an isosceles triangle

5 votes
6 answers
785 views

Problem based on ages of two persons.

5 votes
4 answers
1k views

Prove that: $\sec^2 20^\circ +\sec^2 40^\circ +\sec^2 80^\circ = \textrm 36$

5 votes
5 answers
480 views

If $\tan^{-1} \left(\frac {\sqrt {1+x^2} - \sqrt {1-x^2}}{\sqrt {1+x^2} + \sqrt {1-x^2}}\right) = \alpha$, then prove $x^2=\sin(2\alpha)$

5 votes
3 answers
770 views

In any $\triangle ABC$, prove that: $\frac {\cos B-\cos C}{\cos A +1}=\frac {c-b}{a}$

5 votes
1 answer
2k views

Using Rolle's theorem to show $e^x=1+x$ has only one real root

5 votes
8 answers
208 views

Evaluating: $\int \frac {1+\sin (x)}{1+\cos (x)} dx$

5 votes
2 answers
20k views

The Arithmetic Mean (A.M) between two numbers exceeds their Geometric Mean (G.M.)

5 votes
3 answers
367 views

If $\sin^{-1} (x) + \sin^{-1} (y)+ \sin^{-1} (z)=\dfrac {\pi}{2}$, prove that $x^2+y^2+z^2+2xyz=1$

4 votes
1 answer
287 views

If the sides $a$, $b$ and $c$ of $\triangle ABC$ are in Arithmetic Progression

4 votes
2 answers
71 views

Find $g(2002)$ given $f(1)$ and two inequalities

4 votes
5 answers
269 views

Prove the following determinant

4 votes
3 answers
385 views

If sides $a$, $b$, $c$ of $\triangle ABC$ are in arithmetic progression, then $3\tan\frac{A}{2}\tan\frac {C}{2}=1$

4 votes
3 answers
3k views

Prove that: $\tan^6 20° - 33\tan^4 20° + 27\tan^2 20°=3$

4 votes
1 answer
79 views

A contractor had to finish a work in

4 votes
6 answers
3k views

The digits of a positive integer, having three digits, are in A.P and their sum is $15$. The number ..

4 votes
2 answers
531 views

If $(1+ \cos A) (1+ \cos B) (1+\cos C)= y = (1- \cos A) (1-\cos B) (1-\cos C)$ then prove that $y = \pm \sin A \sin B \sin C$

4 votes
6 answers
3k views

The probability of scoring a 2 just once when a die is thrown three times?

4 votes
2 answers
7k views

Prove that every equation of degree $n$ in $x$ has $n$ roots and no more.

4 votes
5 answers
247 views

If $x^3 - 5x^2+ x=0$ then find the value of $\sqrt {x} + \dfrac {1}{\sqrt {x}}$

3 votes
6 answers
1k views

Evaluate the given limit: $\lim_{x\to \infty} (\sqrt {x-a} - \sqrt {bx})$

3 votes
1 answer
448 views

The circumference of the circle is $C$, what is the area of circle in terms of $C$?

3 votes
6 answers
1k views

Evaluate: $\lim_{\theta \to \frac {\pi}{4}} \dfrac {\cos \theta - \sin \theta}{\theta - \frac {\pi}{4}}$

3 votes
3 answers
128 views

Integrate $\int \frac {1}{(x+2)(x+3)} \textrm {dx}$

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