Tag Archives: Tangent

For which real number x is tan^3(x) + cot^3(x) a prime number?

    Take all real numbers     for which       is a positive integer.   Find those of them for which       is a prime number.       Note that     Any other solutions?   … Continue reading

Posted in Prime Numbers | Tagged , | 2 Comments

Triangle (A,B,C) such that tan A, tan B, and tan C integers?

    For any triangle ABC, the proof can be easily derived from simple trigonometric identities.     Is it possible for all three of   ,   ,   and     to be integers? If so,   how … Continue reading

Posted in Number Puzzles | Tagged | Leave a comment

tan in G.P. and cot in A.P.

  In a triangle ADC,   AD = AC   and   AE   is the altitude CD is extended to point B such that   BA = 10                    

Posted in Geometry | Tagged , | Leave a comment

Area between three tangent circles?

3 circles of radius r such that all three are externally tangent, what is the area of the shape in the center in terms of r?                 What’s the area between three tangent circles?     Area … Continue reading

Posted in Geometry | Tagged , , | 2 Comments