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ICSE Class 10 Answered

If I tan a +m sec a=n and q tan a +r seca =j  then prove that:(nq-qn/mq-rl)^2=1+(jm-rn/mq-lr)^2
Asked by kmondaldgms | 16 Aug, 2018, 11:20: AM
answered-by-expert Expert Answer
begin mathsize 16px style straight l space tana space space space plus space straight m space seca space equals space straight n space space space... left parenthesis straight i right parenthesis straight q space tana space plus space straight r space seca space equals space straight j space space space space space space space... left parenthesis ii right parenthesis To space prove colon space open parentheses fraction numerator nq space minus qn over denominator mq space minus space rl end fraction space close parentheses squared space equals space 1 space plus space open parentheses fraction numerator jm space minus space rn over denominator mq space minus lr end fraction close parentheses squared from space left parenthesis straight i right parenthesis comma tana space equals space fraction numerator straight n space minus space straight m space seca over denominator straight l end fraction space space space space.... left parenthesis iii right parenthesis Put space the space value space of space tana space in space equation space left parenthesis ii right parenthesis comma space we space get straight q open parentheses fraction numerator straight n space minus space mseca over denominator straight l end fraction close parentheses space plus space straight r space seca space equals space straight j rightwards double arrow qn over straight l space minus space fraction numerator qm space seca over denominator straight l end fraction space plus space straight r space seca space equals space straight j rightwards double arrow qn over straight l space minus space seca space open parentheses qm over straight l space minus space straight r close parentheses space equals space straight j rightwards double arrow seca space space equals space fraction numerator begin display style qn over straight l end style space minus space straight j over denominator begin display style qm over straight l end style space minus space straight r end fraction rightwards double arrow seca space equals space fraction numerator qn space minus space jl over denominator qm space minus space rl space space space end fraction space space space space....... left parenthesis iv right parenthesis put space the space value space of space seca space in space equation space left parenthesis iii right parenthesis comma space we space get tana space equals space fraction numerator straight n space minus straight m open parentheses begin display style fraction numerator qn space minus jl over denominator qm space minus space rl end fraction end style close parentheses over denominator straight l end fraction space space space space space space space equals fraction numerator straight n left parenthesis qm space minus space rl right parenthesis minus straight m left parenthesis qn space minus space jl right parenthesis over denominator straight l left parenthesis qm space minus space rl right parenthesis end fraction space space space space space space space after space solving comma space we space get tana space equals space fraction numerator left parenthesis mj space minus space nr right parenthesis over denominator left parenthesis qm space minus space rl right parenthesis end fraction space space space space...... left parenthesis straight v right parenthesis We space know space that comma sec squared straight a space equals space 1 space plus space tan squared straight a from space left parenthesis iv right parenthesis space and space left parenthesis straight v right parenthesis comma space we space get open parentheses fraction numerator nq space minus qn over denominator mq space minus space rl end fraction space close parentheses squared space equals space 1 space plus space open parentheses fraction numerator jm space minus space rn over denominator mq space minus lr end fraction close parentheses squared hence comma space proved. end style
Answered by Yasmeen Khan | 16 Aug, 2018, 02:30: PM

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