Koundinya-Mathematics Teachers Hub

For all the passionate teachers,students and mathematics enthusiasts may this be a platform to interact..

Friday, 20 November 2020

$If \,\,z=r(cos\theta+i\,sin\theta)\,\,and \,\,2w=r\left [ cos\frac{\pi}{4}+\theta+i\,sin(\frac{\pi}{4}+\theta) \right ],\,\, prove \,\,that \\z+w=\frac{r\,cosec\phi}{\sqrt{2}}\left [ cos(\frac{\pi}{4}+\overline{\theta-\phi})+\theta+i\,sin(\frac{\pi}{4}+\overline{\theta-\phi}) \right ]\,\,where \\tan\phi=2-\sqrt{2}$

Posted by Koundinya-Mathematics teacher's hub at 05:18 No comments:

Email This BlogThis!Share to X Share to Facebook Share to Pinterest

$Find\,\, the\,\, values\,\ of\,\, x\,\, satisfying\,\, the\,\, equation\,\, 3^{x}+1-\left | 3^{x}-1 \right |=2log_5^{\left | 6-x \right |}$

Posted by Koundinya-Mathematics teacher's hub at 04:50 No comments:

Email This BlogThis!Share to X Share to Facebook Share to Pinterest

Friday, 13 November 2020

$A\,\,triangle\,\,has\,\,vertices\,\,at\,\,the\,\,points\,\,represented \,\,by\,\, complex\,\, numbers\\Z_{1},\,\,Z_{2},\,\,Z_{3}.\,\,\, Show \,\,that\,\, the\,\, complex\,\, number\,\, associated\,\, with\,\, the \,\,orthocentre\,\, is\\\\ \frac{Z_{1}Tan\,A+Z_{2}Tan\,B+Z_{3}Tan\,C}{Tan\,A+Tan\,B+Tan\,C}$

Posted by Koundinya-Mathematics teacher's hub at 10:01 No comments:

Email This BlogThis!Share to X Share to Facebook Share to Pinterest

$If \,\,a>0, b>0;\, a\neq 1, b\neq 1, \,\,find\,\, the\,\, value\,\, of\,\, p\,\, for\,\, which\,\, the\,\, linear\,\, equations\\ px+(\log_b^a)y+(\log_a^b)z=0\\ x+(\log_a^b)y+(\log_b^a)z=0\\ x+(\log_b^a)y+(\log_a^b)z=0\\ has\,\ a \,\,non-trivial\,\, solution.\,\,What\,\, happens\,\, for\,\, p=1?$

Posted by Koundinya-Mathematics teacher's hub at 09:54 No comments:

Email This BlogThis!Share to X Share to Facebook Share to Pinterest

$Solve \,\,\,\,\,\, \frac{3}{2}\,\log_\frac{1}{4}^{(x+2)^2}-\,3=\log_\frac{1}{4}^{(4-x)^3}-\,\log_{4}^{(x+6)^3}$

Posted by Koundinya-Mathematics teacher's hub at 09:44 No comments:

Email This BlogThis!Share to X Share to Facebook Share to Pinterest

$If \quad S_{n}=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.....\frac{1}{n},\\ \quad \quad S_{n}^{'}=\frac{n+1}{2}-{\frac{1}{n(n-1)}+\frac{2}{(n-1)(n-2)}+.....+\frac{(n-2)}{3.2}},\\ then \,\,prove\,\, that\,\, S_{n}=S_{n}^{'}$

Posted by Koundinya-Mathematics teacher's hub at 09:35 No comments:

Email This BlogThis!Share to X Share to Facebook Share to Pinterest

Monday, 9 November 2020

$For\,\, n,\,\, a\,\, positive\,\, integer \geq 1,\,\, Prove\,\, by\,\, the\,\, method\,\, of\,\, mathematical\,\, induction\,\, that \\ \sum_{r=1}^{n}\frac{1}{sin\,2^{r}\,x}=cot\, x-cot\,2^{n}\,x$

Posted by Koundinya-Mathematics teacher's hub at 04:11 No comments:

Email This BlogThis!Share to X Share to Facebook Share to Pinterest

Older Posts Home

Subscribe to: Posts (Atom)

Popular Posts

Infinite roots of a quadratic equation
Welcome note !!!

For all you passionate teachers and mathematics enthusiasts across the continents concerned with the needs of K-12 students... In the pres...
Reusability or Generalisation of a result in problem solving

Problem Description : Find area of the shaded region ABCD in the figure below. Solution : Observation : We begin with the area ...
Conic Sections and Eccentricity(e)

Let us examine the process of Limit e ---> 1of a conic The X shaped lines that define the surface of the cone are called generators an...
A note on Imaginary points in Coordinate Geometry

The young school boys begin elementary arithmetic where they deal with positive numbers. When introduced to negative numbers they find it di...
A note on Permutations and Combinations

Here is a situation where one answer has many questions. ...Try to add to the list!!!...are these independent of each other?
Area of octagon...

ABCD is a square with length of a side 1 cm. An octagon is formed by lines joining the vertices of the square to the midpoints of opposite ...
problem on probability

Four identical dice are rolled once, find the probability of getting atleast three different numbers.
This should challenge you!!!

Delete 100 digits in the number 12345678910111213141516171819. . . . 96979899100 so that the resultant number has (a) The greatest po...
Problem on Triangle(2)

ABC is an equilateral triangle let point P be inside triangle let D , E , F be feet of perpendiculars from P upon BC , CA, AB respectively...

Search This Blog

Total Pageviews

Blog Archive

▼ 2020 (19)
- ▼ November (12)
- ► October (7)

► 2014 (2)
- ► November (2)

► 2013 (6)
- ► March (6)

► 2012 (15)
- ► November (1)
- ► September (1)
- ► August (6)
- ► July (2)
- ► March (4)
- ► January (1)

► 2011 (15)
- ► December (15)

About Me

View my complete profile

Followers

Watermark theme. Powered by Blogger.