Advertisements
Advertisements
प्रश्न
If y = cos (sin x), show that: `("d"^2"y")/("dx"^2) + "tan x" "dy"/"dx" + "y" "cos"^2"x" = 0`
बेरीज
Advertisements
उत्तर
y = cos (sin x) ....(i)
`"dy"/"dx" = -"sin" ("sin x") "cos x"` ...(ii)
`("d"^2"y")/("dx"^2)` = sin (sin x) sin x - cos x (cos (sin x)) cos x
= sin (sin x) sin x - cos2x.y .....(using (i))
= sin (sin x) cos x `((-"sin x")/"cos x")` - y cos2x
=`"dy"/"dx"` (- tan x) - y cos2x ......(using(ii))
`("d"^2"y")/("dx"^2) + "tan x" "dy"/"dx" + "y" "cos"^2"x" = 0`
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
