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If y =sin (sin x) and (d^(2)y)/(dx^(2))+...

If `y =sin (sin x)` and `(d^(2)y)/(dx^(2))+(dy)/(dx) tan x + f(x) = 0`, then find `f(x)`.

Text Solution

Verified by Experts

The correct Answer is:
`cos^(2)x sin (sin x)`
`(dy)/(dx)=cos (sin x) cos x`
`(d^(2)y)/(dx^(2))=-cos ( sin x) sin x + cos x [-sin (sin x)] cos x`
`therefore" "(d^(2)y)/(dx^(2))+(dy)/(dx)tan x= -c os ( sin x) sin x-cos^(2) x sin (sin x)+cos (sin x )cos x tan x`
`=-cos^(2)x sin (sin x)`
`therefore" "(d^(2)y)/(dx^(2))+(dy)/(dx)tan x + cos^(2)x sin (sin x) =0`
`therefore" "f(x)=cos^(2)x sin (sin x)`
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