I F space A cos open parentheses P close parentheses minus B sin open parentheses P close parentheses equals C space space T H E N space P R O V E A sin open parentheses P close parentheses plus B cos open parentheses P close parentheses equals plus-or-minus square root of A squared plus B squared minus C squared end root

Asked by dalbirgolagarh | 30th Jul, 2015, 04:02: PM

Expert Answer:

L e t space A equals R cos theta space a n d space B equals R sin theta W h e r e space R equals square root of A squared plus B squared end root space a n d space tan theta equals B over A G i v e n space t h a t space A cos P space minus space B sin P equals C rightwards double arrow R cos theta c o s P space minus space R sin theta s i n P equals C rightwards double arrow R open parentheses cos open parentheses theta plus P close parentheses close parentheses equals C.... left parenthesis 1 right parenthesis A sin P plus B cos P equals R c o s theta space s i n P plus R s i n theta space c o s P equals R open parentheses sin open parentheses P plus theta close parentheses close parentheses equals plus-or-minus square root of R squared minus R squared open parentheses c o s squared open parentheses theta plus P close parentheses close parentheses end root equals plus-or-minus square root of R squared minus C squared end root space open parentheses f r o m space left parenthesis 1 right parenthesis close parentheses equals plus-or-minus square root of A squared plus B squared minus C squared end root space left parenthesis P r o v e d right parenthesis

Answered by satyajit samal | 31st Jul, 2015, 10:03: AM

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