1i have edited it manmay...
and in 3rd question.. how can it be e?
1. if A and B are two events such that P(A∩B)=P(A) then P(A/B)=1 or P(B/A)=1??
2. tan x dy/dx-(sec2x)y= sin x
here I.F. is cot x or tan x?
3. dy/dx+y=tan x .. here I.F. is elogx??
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6 Answers
1FOR EQN. OF THE FORM dydx+Ky = c
I.F = e∫kdx sorry mistook. answer is ex.
deleted that post. WAS A TYPO.
12) \frac{dy}{dx}-\frac{sec^{2}x}{tanx}y=\frac{sinx}{tanx}
= \frac{dy}{dx}-\frac{1+tan^{2}x}{tanx}y=cosx
= \frac{dy}{dx}-\left( \frac{1}{tanx}+{tanx}\right)y=cosx
comparing with general form \Rightarrow \frac{dy}{dx}+Ky = C where I.F = e∫K dx
we get I.F. = e^{-\int (cotx+tanx)dx}
= e^{-\int \frac{cosx}{sinx}dx-\int \frac{sinx}{cos x}dx}
= e^{-ln\left|sinx \right|+ln\left|cosx \right|}
= e^{ln\left|cosecx \right|+ln\left|cosx \right|}
= e^{ln (cosecx .cosx)}\Rightarrow e^{log_{e}cotx}\Rightarrow cotx
HENCE I.F. = cot x
