यदि `y=tan x + sec x`, तो सिद्ध कीजिये कि `(d^(2)y)/(dx^(2))=("cos x")/((1-sin c)^(2))`.

यदि `y=tan x + sec x`, तो सिद्ध कीजिये

1.	यदि `y=tan x + sec x`, तो सिद्ध कीजिये कि `(d^(2)y)/(dx^(2))=("cos x")/((1-sin c)^(2))`.
Answer» `y=tanx+secx` या `(dy)/(dx)=sec^(2)x+sec x tanx` या `(dy)/(dx)=secx(sec x+ tan x)` या `(d^(2)y)/(dx^(2))=sec x tan x (sec x + tan x)+sec x (sec x tan x + sec^(2)x)` `=sec x tan x (sec x + tan x ) + sec^(2)x (tan x + sec x)` `=(sec x + tan x) (sec x tan x +sec^(2) x)` `=(sec x + tan x) sec x (tan x + sec x)` `=sec x (sec x + tan x ) ^(2)` `=(1)/(cos x) ((1)/(cos x) + (sin x)/(cos x))^(2)` `=(1+sin x)^(2)/(cosx cos ^(2)x)` `=((1+sinx)^(2))/(cos^(3)x)=((1+sin x)^(2)cos x)/(cos^(4)x)` `=((1+sinx)^(2)cos x)/((1+sinx)^(2)(1-sinx)^(2))` `=(cos x)/((1-sin x)^(2))` ( इति सिध्दम )