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# if x = asecA+btanA and y= atanA+bsecA . prove that x^2 - y^2 = a^2 - b^2

Asked by LakshmiSriram 12th September 2013, 12:46 PM
Given, x = asecA+btanA and y= atanA+bsecA
Now,
LHS = x^2 - y^2
= (asecA+btanA)^2 - (atanA+bsecA)^2
= a^2sec^2A + b^2tan^2A + 2absecAtanA - a^2tan^2A - b^2sec^2A - 2abtanAsecA
= a^2 (sec^2A - tan^2A) + b^2 (tan^2A - sec^2A)
= a^2 (1) + b^2 (-1)                (Since, 1+tan^2A = sec^2A)
= a^2 - b^2
= RHS
Answered by Expert 12th September 2013, 10:28 PM
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