find sin(arctan(2) ) let A = arctan(2) ------------------(1) tanA = 2 = 2 / 1 use these on a triangle with side opposite to A as 2, adjacent to A as 1 use pythagoras theorem to get the hypotenuse sqrt(5)
so sin A = 2 / sqrt(5)
using equation(1) sin ( arctan(2) ) = 2 / sqrt(5) = [ 2*sqrt(5) ] / 5
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using three terms of the binomial expansion of 1 / sqrt[ 1 - x^3] , evaluate the integral of 1 / sqrt[ 1 - x^3] with limits 0 to 0.5
binomial series is here n = -1/2 , x should be replaced with ( - x^3)
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Cricket is a game which is popular in India. It is also popular in england, australia, west indies, new zealand,sri lanka, pakistan, bangladesh, south africa, zimbabwe and in most of the former colonies of britain. The older format is test cricket played over a period of five days, consisting of a maximum possible of two innings per team. The shorter formats are mainly 50 over a side one-dayers (usually takes around 7 hours) and the still shorter 20 over a side 20-20. live cricket scores are usually available at cricinfo.com icc test rankings are usually available at icc-cricket.yahoo.net
in the old days test cricket played in india was usually shown live on doordarshan but after large scale commercialisation, it shifted to private pay channels like star sports soon after espn came into the picture after that many other sports channels like ten sports, star cricket, zee sports channel, neo sports have come up. even some channels like set max and sahara which usually show so called hindi serials/ films etc have to subscribed to if you want to watch some of the cricket matches a list of some tv channels available in india
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1. A man working alone can do a piece of work in 20 days while a woman working alone can do the same piece of work in 30 days. In how many days will the work be completed if the man and woman work together?
2. 'A' can do a piece of work in 9 days. If 'B' is 50% more efficient than A, find the number of days required by B to complete the piece of work?
3.A and B can respectively do a piece of work in 20/3 days and 5 days. They work together for 2 days and then A leaves . How many more days will it take for B to complete the work?
4. If 3 men and 5 women can do a piece of work in 8 days, and 2 men and 7 children can do the same piece of work in 12 days, then find how many children's work in a day is equal to the work of 10 women in a day?
5.Two pipes A and B can separately fill a tank in 12 hours and 16 hours respectively. A third pipe C can empty the tank in 8 hours. If all the three pipes are left open, how much time will it take for the tank to be filled?
6. A garrison has enough food for 52 days. After 20 days, 400 more soldiers arrived at the garrison. Now for the increased number of soldiers the food will last for only 24 days. How many soldiers were there originally in the garrison?
7. 40 men can dig a ditch 20m X 10m X 1m in 50 days. How many men will be required to dig another ditch 25m X 8m X 1m in 40 days ?
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If k is an eigen value of a non singular matrix , then (1 / k) is an eigen value of its inverse
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change one of the factors into 1+ tan²x split into two integrals one is a direct formula integration formulae
for the other integral use substitution method ----------------------------------------------------------- please leave your comments below ------------------------------------------------------------ index of math problems
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let A = arctan(2) ------------------(1)
