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CBSE Class 10 Answered

If cosecA - sinA = m and secA - cosA=n Prove that: m^2n raised to 2/3 + mn^2 raised to 2/3 = 1
Asked by manasvi.gopani | 14 Feb, 2018, 12:40: PM
answered-by-expert Expert Answer
begin mathsize 16px style cosecA minus sinA equals straight m
straight m equals 1 over sinA minus sinA
straight m equals fraction numerator 1 minus sin squared straight A over denominator sinA end fraction equals open parentheses fraction numerator cos squared straight A over denominator sinA end fraction close parentheses
straight n equals open parentheses fraction numerator sin squared straight A over denominator cosA end fraction close parentheses
open parentheses straight m squared straight n close parentheses to the power of 2 over 3 end exponent plus open parentheses mn squared close parentheses to the power of 2 over 3 end exponent
equals open parentheses open parentheses fraction numerator cos squared straight A over denominator sinA end fraction close parentheses squared cross times open parentheses fraction numerator sin squared straight A over denominator cosA end fraction close parentheses close parentheses to the power of 2 over 3 end exponent plus open parentheses open parentheses fraction numerator cos squared straight A over denominator sinA end fraction close parentheses cross times open parentheses fraction numerator sin squared straight A over denominator cosA end fraction close parentheses squared close parentheses to the power of 2 over 3 end exponent
equals open parentheses cos cubed straight A close parentheses to the power of 2 over 3 end exponent plus open parentheses sin cubed straight A close parentheses to the power of 2 over 3 end exponent
equals 1 end style
Answered by Arun | 14 Feb, 2018, 02:54: PM
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