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if y=log sqrt(1+tan x/1-tan x)) prove that dy/dx=sec 2x

if y=log sqrt(1+tan x/1-tan x)) prove that dy/dx=sec 2x

Grade:12

2 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago

y=log sqrt(1+tan x/1-tan x))

dy/dx=logv[(tanp/4 +tanx)/(1-tanp/4.tanx)]

=logvtan(p/4+x)

=logtan(p/4+x)1/2

=(1/2). log tan(p/4+x)

Now diff.w.r. to x , we get

Dy/dx=(1/2). 1/tan(p/4+x) . sec2(p/4+x) .1

=(1/2).cos(p/4+x)/sin(p/4+x).1/cos2(p/4+x)

=1/[2sin(p/4+x)cos(p4+x)]

=1/sin(2p/4+2x)

=1/sin(p/2+2x)

=1/cos2x

=sec2x


Thanks & Regards

Rinkoo Gupta

AskIITians Faculty

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hi


Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

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