Prove that cos pi/11 + cos 3pi/11 + cos 5pi/11 + cos 7pi/11 + cos 9pi/11...

A elegant solution for a difficult trigonometric problem using complex numbers. Many problem of trigonometry and even algebra can be beautifully solved using complex numbers. The use of different formulas from trigonometry can be avoided. #CBSE #ISC #IIT #ISI #wbjee #wbchse #jeeadvanced Prove that cos pi/11 + cos 3pi/11 + cos 5pi/11 + cos 7pi/11 + cos 9pi/11 =1/2

Integrate max { x+|x|,x-[x] } from -n to n JEE Main and Advance and Indian Statistical Institute B.Math & B.Stat

Integrate max { x+|x|,x-[x] } from -n to n Difficult Integration for JEE Main and Advance and Indian Statistical Institute Involving Limits Integration for Indian Statistical Institute B.Math & B.Stat : Integration, JEE Main and Advance, WBJEE #CBSE #ISC #wbchse #HS #jeeadvanced

A challenging problem from Geometry

 

The triangle ABC is given. Let T be circle passing through vertex A and intersecting sides AB and AC in points D and E respectively. Let T' be circle passing through vertex B and point D, intersecting side BC and the circle T in points F and T, respectively. Prove that the quadrilateral CEFT is cyclic.

For solution click here: Solution

Term of a sequence 1,2,2,3,3,3,4,4,4,4....

Can you solve this problem? In #mathematics, a #sequence is an enumerated collection of objects in which repetitions are allowed and order does matter. Like a set, it contains members (also called elements, or terms).
#Solution https://t.me/PrimeMaths/50
#PrimeMaths #Algebra

Gergonne triangle

The Gergonne triangle of triangle ABC is defined by the three touchpoints of the incircle on the three sides. This Gergonne triangle, is also known as the contact triangle or intouch triangle of triangle ABC.

#Solution: https://t.me/PrimeMaths/47

#Geometry #PrimeMaths

Powers of 2

A #Number #Theory gem based on #PigeonHole principle.

Prove that there exist two powers of 2 which differ by a multiple of 2020.

#PrimeMaths #Integers #Divisibility

More Problems for Practice:

Problem 1. Prove that of any 52 integers, two can always be found such that the difference of their squares is divisible by 100.

Problem 2. 15 boys gathered 100 nuts. Prove that some pair of buys gathered an identical number of nuts.

Problem 3. Given 11 different natural numbers, none greater than 20. Prove that two of these can be chosen, on of which divides the other.