If y = sin (sin x), prove that d2y/dx2 + (tan x) dy/dx + y cos2 x = 0 - Maths - Continuity and Differentiability

Question

If y = sin (sin x), prove that
d2y/dx2 + (tan x) dy/dx + y
cos2 x = 0

Anuradha Sharma · Accepted Answer

Given y = sinsinxSo dydx= cossinx×ddxsinx=cossinx
cosxAgain differentiating we get, d2ydx2=cossinx×-sinx+cosx×-sinsinx×cos x =-cosxcossinx×sinxcosx-ycos2x=-tanxdydx-ycos2xor d2ydx2+tanxdydx+ycos2x=0

If y = sin (sin x), prove that d2y/dx2 + (tan x) dy/dx + y cos2 x = 0.

If y = sin (sin x), prove that

d²y/dx² + (tan x) dy/dx + y cos² x = 0.