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CBSE Class 10 Answered

If tanΦ + sinΦ =m and  tanΦ-sinΦ = n,  show that m²-n² = 4√mn
Asked by pdcavita | 08 Feb, 2018, 07:57: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight L. straight H. straight S.
equals straight m squared minus straight n squared
equals left parenthesis straight m minus straight n right parenthesis left parenthesis straight m plus straight n right parenthesis
equals left parenthesis tan space straight ϕ plus sin space straight ϕ minus tan space straight ϕ plus sin space straight ϕ right parenthesis left parenthesis tan space straight ϕ plus sin space straight ϕ plus tan space straight ϕ minus sin space straight ϕ right parenthesis
equals 2 sin space straight ϕ cross times 2 tan space straight ϕ
equals 4 space tan space straight ϕ space sin space straight ϕ
equals 4 square root of tan squared space straight ϕ space sin squared space straight ϕ end root
equals 4 square root of tan squared space straight ϕ space left parenthesis 1 minus cos squared space straight ϕ right parenthesis end root
equals 4 square root of tan squared space straight ϕ minus tan squared space straight ϕ space cos squared space straight ϕ end root
equals 4 square root of tan squared space straight ϕ minus fraction numerator sin squared space straight ϕ over denominator cos squared space straight ϕ end fraction cross times cos squared space straight ϕ end root
equals 4 square root of tan squared space straight ϕ minus sin squared space straight ϕ end root
equals 4 square root of left parenthesis tan space straight ϕ plus sin space straight ϕ right parenthesis left parenthesis tan space straight ϕ minus sin space straight ϕ right parenthesis end root
equals 4 square root of mn end style
Answered by Rashmi Khot | 09 Feb, 2018, 09:42: AM

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