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Please observe the question carefully and then answer :  cos^4A/cos^2B + sin^4A/sin^2B=1  then prove that : cos^4B/cos^2A + sin^4B/sin^2A =1
Asked by guptaabhinav0809 | 28 Feb, 2019, 09:59: AM
answered-by-expert Expert Answer
begin mathsize 12px style fraction numerator cos to the power of 4 A over denominator cos squared B end fraction plus fraction numerator begin display style sin to the power of 4 A end style over denominator begin display style sin squared B end style end fraction space equals space 1 equals fraction numerator cos to the power of 4 A space sin squared B space plus sin to the power of 4 A space cos squared B space over denominator cos squared B space sin squared B end fraction space equals space 1 h e n c e comma space space space space cos to the power of 4 A space sin squared B space plus sin to the power of 4 A space cos squared B space equals space cos squared B space sin squared B B y space c o n v e r t i n g space a l l space t h e space t e r m s space i n space t e r m s space o f space cos comma space w e space g e t space cos to the power of 4 A space open parentheses 1 space minus space cos squared B close parentheses space plus open parentheses 1 minus cos squared A close parentheses squared space cos squared B space equals space cos squared B space open parentheses 1 minus cos squared B close parentheses cos to the power of 4 A space minus space cos to the power of 4 A space cos squared B space plus space open parentheses 1 plus space cos to the power of 4 A space minus space 2 space cos squared A close parentheses cos squared B space equals space cos squared B space minus space cos to the power of 4 B cos to the power of 4 A space minus space cos to the power of 4 A space cos squared B space plus space cos squared B space plus space cos to the power of 4 A space cos squared B space space minus space 2 space cos squared A space cos squared B space space equals space cos squared B space minus space cos to the power of 4 B cos to the power of 4 A space space space minus space 2 space cos squared A space cos squared B space space plus space space cos to the power of 4 B space equals space open parentheses cos squared A space minus space cos squared B close parentheses equals 0 H e n c e space A space equals space B end style
 
since A = B, in the given eqn. begin mathsize 12px style fraction numerator cos to the power of 4 A over denominator cos squared B end fraction plus space fraction numerator begin display style sin to the power of 4 end style begin display style A end style over denominator begin display style sin squared end style begin display style B end style end fraction space equals space 1 end style   , if we replace A = B, Then we get begin mathsize 12px style fraction numerator cos to the power of 4 B over denominator cos squared A end fraction plus space fraction numerator begin display style sin to the power of 4 B end style over denominator begin display style sin squared A end style end fraction space equals space 1 end style
Answered by Thiyagarajan K | 28 Feb, 2019, 12:59: PM

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