secx - cosecx = 4/3
sinx - cosx =?
 

Asked by Sugandha | 27th Apr, 2017, 02:48: PM

Expert Answer:

begin mathsize 16px style secx minus cosecx equals 4 over 3
1 over cosx minus 1 over sinx equals 4 over 3
sinx minus cosx equals 4 over 3 sinxcosx........... left parenthesis straight i right parenthesis
Consider comma
secx minus cosecx equals 4 over 3
squaring space on space both space sides comma
sec squared straight x plus cosec squared straight x minus 2 secxcosecx equals 16 over 9
fraction numerator 1 over denominator cos squared straight x end fraction plus fraction numerator 1 over denominator sin squared straight x end fraction minus 2 over sinxcosx equals 16 over 9
fraction numerator sin squared straight x plus cos squared straight x over denominator left parenthesis sinxcosx right parenthesis squared end fraction minus 2 over sinxcosx equals 16 over 9
fraction numerator 1 over denominator left parenthesis sinxcosx right parenthesis squared end fraction minus 2 over sinxcosx equals 16 over 9
take space 1 over sinxcosx equals straight m space and space solve space for space quadratic space equation space you space will space get space
straight m equals sinxcosx equals 3 over 8 space or space fraction numerator negative 3 over denominator 2 end fraction
Put space it space in space left parenthesis straight i right parenthesis space you space will space get
sinx minus cosx equals 1 half space or space minus 2

end style

Answered by Sneha shidid | 29th Apr, 2017, 09:44: AM