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CBSE Class 12 Math 2018 Solved Paper

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Question : 15
Total: 29
if y = sin (sin x), prove that
d2y
dx2
 + tan x
dy
dx
 + y cos2 x = 0
Solution:  
y = sin (sin x)
dy
dx
 = cos (sin x) . cos x
d2y
dx2
 = cos (sin x) - . (- sin x) + cos x . (- si (sin x). cos x)
d2y
dx2
 = - sin x . cos (sin x) - y cos2 x
now,
d2y
dx2
 + tan x
dy
dx
 + y cos2 x
= - sin x . cos (sin x) - y cos2 x + tan x . cos (sin x) . cos x + y cos2 x
= - sin x . cos (sin x) - y cos2 x +
sinx
cosx
 . cos (sin x) . cos x + y cos2 x
= 0
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