If y = etan x, then (cos2 x)y2 =

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KollegeApply · Accepted Answer

(c) (1 + sin 2x)y1 Here y = e^{\tan x} \Rightarrow y_1 = e^{\tan x } \sec^2 x \Rightarrow y_2 = e^{\tan x } \sec^4 x + e^{\tan x} $\times$ 2\sec x \sec x \tan x \Rightarrow y_2 = \sec^2 x\left( e^{\tan x} \sec^2 x + e^{\tan x } $\times$ 2 \tan x \right) \Rightarrow \left( \cos^2 x \right) y_2 = y_1 + e^{\tan x } $\times$ y_1/\sec^2 x2 \tan x \Rightarrow \left( \cos^2 x \right) y_2 = y_1 + y_1 $\times$ 2 \sin x \cos x \Rightarrow \left( \cos^2 x \right) y_2 = y_1 \left( 1 + \sin2x \right)

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