If `y=e^(tanx)` , then `(cos^2x)y_2=` `(1-sin2x)y_1` (b) `-(1+sin2x)y_1` (c) `(1+sin2x)y_1` (d) none of these

Explanation

Correct Answer Is (C)

` (1+sin 2 x) y_{1}`

Given:
`
y=e^{tan x}`
`
frac{d y}{d x}=e^{tan x}(sec x)^{2}`
`
frac{d^{2} y}{d x^{2}}=e^{tan x}(sec x)^{2}(sec x)^{2}+e^{tan x} times 2 sec x times tan x times sec x`
`
={e}^{tan x}(sec x)^{2}[(sec x)^{2}+2 tan x] `
`
(cos ^{2} x) y_{2}=e^{tan x}[(sec x)^{2}+2 tan x] `
`
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