Question

If y = sec x-tan x, prove that cos x d^2y/dx^2=y^2
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Answer 1

y = sec x - tan x

d y/d x = sec x tan x - sec^2x

d y/d x = sec x (tan x - sec x)

d y/d x = -y sec x

d^2y/dx^2 = -sec x dy/dx - y sec x tan x

d^2y/dx^2 = sec x (y secx - y tan x )

cos x d^2y/dx^2 = y (sec x - tan x) = y^2