CBSE Class 11-science Answered
if tan x=a/a+1 and tan y=1/2a+1
prove that x+y= ?/4.
Asked by ripan kaur | 22 May, 2011, 12:28: AM
Expert Answer
tanx = a/(a+1).
tany = 1/(2a+1).
We know that tan (x+y) = (tanx+tany)/(1-tanx*tany) is an identity.
=> tan(x+y) = {a/(a+1) +1/(2a+1)}/{ 1- a/(a+1)(2a+1)}.
=> tan(x+y) = {a(2a+1)+a+1}/{(2a+1)(a+1)-1}.
=> tan (x+y) = (2a^2+2a+1)/{2a^2+3a+1-a}.
=> tan(x+y) = (2a^2+2a+1)/(2a^2+2a+1) = 1.
=> tan(x+y) = 1.
Therefore x+y = arc tan 1 = pi/4.
Therefore x+y = pi/4
Answered by | 22 May, 2011, 04:42: PM
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