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Question
If y = tan x + sec x then prove that `(d^2y)/(dx^2) = cosx/(1 - sinx)^2`.
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Solution
y = tan x + sec x
`dy/dx = d/dx (tan x) + d/dx (sec x)`
= sec2 x + sec x tan x
= sec x (sec x + tan x)
= `1/cosx(1/cosx + sinx/cosx)`
= `(1 + sinx)/(cos^2x)`
`dy/dx = (1 + sinx)/(1 - sin^2x)`
= `1/(1 - sinx)`
`(d^2y)/(dx^2) = ((1 - sinx)0 - 1(-cosx))/(1 - sinx)^2`
= `cosx/(1 - sinx)^2`.
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