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CBSE Class 11-science Answered

 
 
Asked by Sukrit Saha | 19 Jul, 2016, 10:29: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight x over straight a equals cos left parenthesis straight theta minus straight alpha right parenthesis comma space straight y over straight b equals cos left parenthesis straight theta minus straight beta right parenthesis LHS equals open parentheses straight x over straight a close parentheses squared plus open parentheses straight y over straight b close parentheses squared minus 2 open parentheses straight x over straight a close parentheses open parentheses straight y over straight b close parentheses cos left parenthesis straight alpha minus straight beta right parenthesis space space space space space space space space equals cos squared left parenthesis straight theta minus straight alpha right parenthesis plus cos squared left parenthesis straight theta minus straight beta right parenthesis minus 2 space cos left parenthesis straight theta minus straight alpha right parenthesis cos left parenthesis straight theta minus straight beta right parenthesis cos left parenthesis straight alpha minus straight beta right parenthesis space space space space space space space space equals cos squared left parenthesis straight theta minus straight alpha right parenthesis plus cos squared left parenthesis straight theta minus straight beta right parenthesis minus 2 space cos left parenthesis straight theta minus straight alpha right parenthesis cos left parenthesis straight theta minus straight beta right parenthesis cos open square brackets left parenthesis straight theta minus straight beta right parenthesis minus left parenthesis straight theta minus straight alpha right parenthesis close square brackets space space space space space space space space equals cos squared left parenthesis straight theta minus straight alpha right parenthesis plus cos squared left parenthesis straight theta minus straight beta right parenthesis minus 2 space cos left parenthesis straight theta minus straight alpha right parenthesis cos left parenthesis straight theta minus straight beta right parenthesis left square bracket cos left parenthesis straight theta minus straight beta right parenthesis cos left parenthesis straight theta minus straight alpha right parenthesis plus sin left parenthesis straight theta minus straight alpha right parenthesis sin left parenthesis straight theta minus straight beta right parenthesis right square bracket space space space space space space space space equals cos squared left parenthesis straight theta minus straight alpha right parenthesis plus cos squared left parenthesis straight theta minus straight beta right parenthesis minus 2 space cos squared left parenthesis straight theta minus straight alpha right parenthesis cos squared left parenthesis straight theta minus straight beta right parenthesis minus 2 cos left parenthesis straight theta minus straight alpha right parenthesis sin left parenthesis straight theta minus straight alpha right parenthesis cos left parenthesis straight theta minus straight beta right parenthesis sin left parenthesis straight theta minus straight beta right parenthesis RHS equals sin squared left parenthesis straight alpha minus straight beta right parenthesis space space space space space space space space equals left square bracket sin left square bracket left parenthesis straight theta minus straight beta right parenthesis minus left parenthesis straight theta minus straight alpha right parenthesis right square bracket right square bracket squared space space space space space space space space equals left square bracket sin left square bracket left parenthesis straight theta minus straight beta right parenthesis cos left parenthesis straight theta minus straight alpha right parenthesis minus cos left parenthesis straight theta minus straight beta right parenthesis sin left parenthesis straight theta minus straight alpha right parenthesis right square bracket right square bracket squared space space space space space space space space equals sin squared left parenthesis straight theta minus straight beta right parenthesis cos squared left parenthesis straight theta minus straight alpha right parenthesis plus cos squared left parenthesis straight theta minus straight beta right parenthesis sin squared left parenthesis straight theta minus straight alpha right parenthesis minus 2 sin left parenthesis straight theta minus straight beta right parenthesis cos left parenthesis straight theta minus straight alpha right parenthesis cos left parenthesis straight theta minus straight beta right parenthesis sin left parenthesis straight theta minus straight alpha right parenthesis space space space space space space space space equals left square bracket 1 minus cos squared left parenthesis straight theta minus straight beta right parenthesis right square bracket cos squared left parenthesis straight theta minus straight alpha right parenthesis plus left square bracket left square bracket 1 minus cos squared left parenthesis straight theta minus straight alpha right parenthesis right square bracket right square bracket cos squared left parenthesis straight theta minus straight beta right parenthesis minus 2 sin left parenthesis straight theta minus straight beta right parenthesis cos left parenthesis straight theta minus straight alpha right parenthesis cos left parenthesis straight theta minus straight beta right parenthesis sin left parenthesis straight theta minus straight alpha right parenthesis space space space space space space space space equals cos squared left parenthesis straight theta minus straight alpha right parenthesis plus cos squared left parenthesis straight theta minus straight beta right parenthesis minus 2 cos squared left parenthesis straight theta minus straight alpha right parenthesis cos squared left parenthesis straight theta minus straight beta right parenthesis minus 2 sin left parenthesis straight theta minus straight beta right parenthesis cos left parenthesis straight theta minus straight alpha right parenthesis cos left parenthesis straight theta minus straight beta right parenthesis sin left parenthesis straight theta minus straight alpha right parenthesis space space space space space space space space equals LHS Hence space proved. end style
Answered by Rebecca Fernandes | 22 Jul, 2016, 09:10: AM

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