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icse maths trigno question | solved |

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abhas
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PostSubject: 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




PostSubject: 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




PostSubject: Re: icse maths trigno question | solved | Thu May 05, 2011 6:38 pm

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