यदि ` y = sin ( sin x) ` तो सिद्ध कीजिए कि ` y_(2) +y_(1) tan x + y cos^(2) x = 0 `

Explanation

दिया है ` y sin (sin x) `
`y_(1) [ cos (sin x)] cos x`
पुनः अवकलन करने पर
` y^(2) = [cos (sin x) ]. ( -sinx) + cos x. [-sin ( sin x) ] cos x`
` = -sin x cos (sin x) - cos^(2) x sin ( sin x) `
` = -sin x cos (sin x) - y cos^(2) x, " " [ :' y = sin ( sin x)]`
` = -sin x y/(cos x) - y cos^(2) x,` [(1) से]
अतः ` y^(2) + y_(1) tan x + y cos ^(2) x = 0 `