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ICSE Class 10 Answered

if a sec theta +b tan theta +c=0 and p sec theta +qtan theta +r =0 then prove that (br-qc)^2 -(pc-ar)^2=(aq-bp)^2
Asked by kmondaldgms | 17 Aug, 2018, 12:04: AM
answered-by-expert Expert Answer
begin mathsize 16px style straight a space secθ space plus space straight b space tanθ space plus space straight c space equals space 0
rightwards double arrow straight c space equals space minus left parenthesis straight a space secθ space plus space straight b space tanθ right parenthesis
straight p space secθ space plus space straight q space tanθ space space plus space straight r space equals space 0
rightwards double arrow space straight r space equals space minus left parenthesis straight p space secθ space plus space straight q space tanθ right parenthesis
straight L. straight H. straight S space equals left parenthesis br space minus space qc right parenthesis squared space minus space left parenthesis pc space minus space ar right parenthesis squared
space space space space space space space space space equals open square brackets straight b open parentheses negative straight p space secθ space minus space straight q space tanθ close parentheses minus space straight q open parentheses negative straight a space secθ space minus space straight b space tanθ close parentheses close square brackets minus
space space space space space space space space space space space space space open square brackets straight p open parentheses negative straight a space secθ space minus space straight b space tanθ close parentheses space minus space straight a open parentheses negative straight p space secθ space minus space straight q space tanθ close parentheses close square brackets
space space space space space space space space space space space space space after space solving comma space we space get
space space space space space space space space space equals left parenthesis aq space minus space bp right parenthesis squared left parenthesis sec squared straight theta space minus space tan squared straight theta right parenthesis
space space space space space space space space space equals left parenthesis aq space minus space bp right parenthesis squared space space space space space space space space.... since comma space sec squared straight theta space minus space tan squared straight theta space equals space 1
space space space space space space space space space equals straight R. straight H. straight S
Hence comma space proved.

end style
Answered by Yasmeen Khan | 17 Aug, 2018, 11:31: AM
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