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if a=secA-tanA , b=cosecA+cotA then a= interms of b

Asked by bugadasuvarna 4th January 2018, 9:16 PM
Answered by Expert
Answer:
begin mathsize 16px style cosec space straight a plus cot space straight a equals straight b space horizontal ellipsis left parenthesis 1 right parenthesis space
now comma space cosec squared straight a space – space cot squared straight a space equals space 1 space space space space space space
or comma space left parenthesis cosec space straight a plus cot space straight a right parenthesis space space left parenthesis cosec space straight a minus cot space straight a right parenthesis space equals space 1 space
or comma space straight b left parenthesis cosec space straight a minus cot space straight a right parenthesis equals 1 space or comma space
cosec space straight a minus cot space straight a space equals space 1 over straight b space space space... left parenthesis 2 right parenthesis space space space
add space eqn space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis space
cosec space straight a space plus space cot space straight a space plus space cosec space straight a space – space cot space straight a space equals fraction numerator straight b squared plus 1 over denominator straight b end fraction
or comma space 2 cosec space straight a space equals space fraction numerator straight b squared plus 1 over denominator straight b end fraction space or comma space
fraction numerator 2 over denominator sin space straight a end fraction equals space fraction numerator straight b squared plus 1 over denominator straight b end fraction
or comma space sina space equals space fraction numerator straight b over denominator straight b squared plus 1 end fraction
now comma space left parenthesis 1 right parenthesis space – space left parenthesis 2 right parenthesis space
cosec space straight a space plus space cot space straight a space – space cosec space straight a space plus space cot space straight a space equals space fraction numerator straight b squared minus 1 over denominator straight b end fraction
or comma space 2 cot space straight a space equals space fraction numerator straight b squared minus 1 over denominator straight b end fraction
or comma fraction numerator space 2 cos space straight a over denominator sin space straight a end fraction space equals space fraction numerator straight b squared minus 1 over denominator straight b end fraction
or comma space fraction numerator space 2 cos space straight a over denominator fraction numerator straight b over denominator straight b squared plus 1 end fraction end fraction space equals space fraction numerator straight b squared minus 1 over denominator straight b end fraction
or comma space cos space straight a space equals space fraction numerator straight b squared minus 1 over denominator straight b squared plus 1 end fraction
or comma space sec space straight a space equals space fraction numerator straight b squared plus 1 over denominator straight b squared minus 1 end fraction space space space horizontal ellipsis left parenthesis 3 right parenthesis space space space
tan space straight a equals fraction numerator space fraction numerator straight b over denominator straight b squared plus 1 end fraction over denominator fraction numerator straight b squared minus 1 over denominator straight b squared plus 1 end fraction end fraction equals fraction numerator straight b cubed plus straight b over denominator straight b to the power of 4 minus 1 end fraction
now comma
sec space straight a minus space tan space straight a equals straight a space horizontal ellipsis left parenthesis 1 right parenthesis space
space fraction numerator straight b squared plus 1 over denominator straight b squared minus 1 end fraction minus fraction numerator straight b cubed plus straight b over denominator straight b to the power of 4 minus 1 end fraction equals straight a
simplify end style
Answered by Expert 19th January 2018, 6:59 PM
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