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if y=tanx+secx then proove that d²y/dx²=cosx/(1-sinx)²

if y=tanx+secx then proove that d²y/dx²=cosx/(1-sinx)²

Grade:12

2 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
dwr to x
            y'= Sec^2 x + Sec x tan x = y Sec x
            y” = y sec x tan x + y'sec x
                =  sec x ( ytanx + y')
                 = sec x ( tan^2x + sec x tan x + sec x tan x + sec^2 x)
                 = sec x ( sec x + tan x )^2
                 = (1/cos x)( 1+ Sin x/Cosx )^2
                 = (1+Sin x)^2/ Cos^3 x
                 = (1+Sin x)^2. (1-Sin x)^2/Cos^3 x (1-Sin x)^2
                 = Cos^4 x / Cos^3 x (1-Sin x)^2
                 = Cos x / (1-Sin x)^2.    
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)
ankit singh
askIITians Faculty 614 Points
3 years ago
this is thesimplest
y'= Sec^2 x + Sec x tan x = y Sec x
            y” = y sec x tan x + y'sec x
                =  sec x ( ytanx + y')
                 = sec x ( tan^2x + sec x tan x + sec x tan x + sec^2 x)
                 = sec x ( sec x + tan x )^2
                 = (1/cos x)( 1+ Sin x/Cosx )^2
                 = (1+Sin x)^2/ Cos^3 x
                 = (1+Sin x)^2. (1-Sin x)^2/Cos^3 x (1-Sin x)^2
                 = Cos^4 x / Cos^3 x (1-Sin x)^2
                 = Cos x / (1-Sin x)^2.   
method to solve this type of
question please look it carefully         thank u
regards ankit singh manit bhopal

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