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the equation xtanx + tanx - k - kx + lxl +xlxl =0,in (0, pi/2 ) has only one solution then the value of k may be (a) 2, (b) -2 (c) 1 (d) -1

the equation xtanx + tanx - k - kx + lxl +xlxl =0,in (0, pi/2 ) has only one solution then the value of k may be
(a) 2, (b) -2 (c) 1 (d) -1

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago
THe equation :
xtanx + tanx - k - kx + x + x*x =0 , as x is in range (0,pi/2)
So, tanx(x+1) - k(x+1) + x(x+1) =0
(x+1) ( tan x + x - k) = 0
Either x + 1 =0 which is not possible as x= -1
So, tan x + x = k
k may be 1 or 2. Positive values.
So, (a) and (c) both.
Thanks & Regards
Bharat Bajaj
askIITians Faculty
IIT Delhi

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