abhas Active member
| Subject: icse maths trigno question | solved | Tue Dec 02, 2008 1:17 pm | |
| Given :- tan A + cot A = 2
Prove that :- (tan A)^n +(cot A)^n = 2
This is the solution.
tan A + cot A = 2 => (tan A)^2 + (cot A)^2 +2tan Acot A = 4 => (tan A)^2 + (cot A)^2 +2 = 4 [tan A * cot A = 1] => (tan A)^2 + (cot A)^2 = 2 => (tan A)^2 + (cot A)^2 -2= 0 => (tan A)^2 + (cot A)^2 -2tan A cot A= 0 [tan A * cot A = 1] => (tan A - cot A)^2=0 => tan A - cot A = 0 => tan A = cot A
tan A + cot A = 2 => tan A + tan A = 2 [tan A= cot A] => 2 tan A = 2 => tan A = 1 Therefore cot A = 1
(tan A)^n + (cot A)^n = (1)^n + (1)^n [tan A = cot A = 1] = 1 + 1 =2
Hence (tan A)^n + (cot A)^n = 2 proved. |
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Mathelp
| Subject: Re: icse maths trigno question | solved | Tue Sep 07, 2010 5:52 pm | |
| Hi, Good solution. I never thought this way. For more practice tests check: Maths Online Test . These tests are really helpful. |
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johnbreckan
| Subject: Re: icse maths trigno question | solved | Thu May 05, 2011 6:38 pm | |
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| Subject: Re: icse maths trigno question | solved | | |
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