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ICSE Class 8 Answered

If cosA = ncosB and sinA = msinB then show that (m^2-n^2)sin^2B =1-n^2
Asked by venkat.gunuganti | 19 May, 2019, 11:55: AM
answered-by-expert Expert Answer
begin mathsize 16px style cosA space equals space ncosB space and space sinA space equals space msinB
rightwards double arrow straight n space equals space cosA over cosB space space and space straight m space equals sinA over sinB space
straight L. straight H. straight S space equals space left parenthesis straight m squared minus straight n squared right parenthesis sin squared straight B
space space space space space space space space space space space space equals open square brackets space open parentheses sinA over sinB close parentheses squared space minus space open parentheses cosA over cosB close parentheses squared close square brackets sin squared straight B
space space space space space space space space space space space space equals fraction numerator sin squared Acos squared straight B minus space cos squared Asin squared straight B over denominator sin squared Bcos squared straight B end fraction cross times sin squared straight B
space space space space space space space space space space space space equals sin squared straight A space minus space cos squared Atan squared straight B
space space space space space space space space space space space space equals open parentheses 1 space minus space cos squared straight A space minus cos squared Atan squared straight B space close parentheses
space space space space space space space space space space space space equals open square brackets 1 space minus cos squared straight A open parentheses 1 space space plus space tan squared straight B space close parentheses space close square brackets
space space space space space space space space space space space space equals space 1 space minus space cos squared Asec squared straight B
space space space space space space space space space space space space equals space 1 space minus space fraction numerator cos squared straight A over denominator cos squared straight B end fraction
space space space space space space space space space space space equals space 1 space minus space straight n squared
space space space space space space space space space space space equals space straight R. straight H. straight s end style
Answered by Yasmeen Khan | 19 May, 2019, 04:40: PM
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