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Question
If y = tan x, then prove that y2 - 2yy1 = 0.
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Solution
Given y = tan x ...(1)
Differentiating with respect to 'x' we get,
`y_1 = "dy"/"dx" = sec^2x` ....(2)
Differentiating again with respect to 'x' we get,
`y_2 = ("d"^2y)/"dx"^2 = 2 sec x "d"/"dx" (sec x)`
y2 = 2 sec x . sec x tan x
= 2 sec2x tan x
= 2y1y ...[using (1) and (2)]
⇒ y2 - 2yy1 = 0
Hence proved.
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