diffrential equations error ( class 12 cbse)

[silent hill]

isnt this wrong , isnt sinx/tanx = cosx

brainly link = https://brainly.in/question/6164199

the original question is a linear diffrentiation q

( y - sin x)dx + tanx dy

can someone show me the working thanks coz the answer in my book is logsecx/sinx

[frigid osprey]

<@&1227988399579730072>

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[languid swan]

<@&1227988399579730072> any inputs?

[lime ether]

Yes, but the approach is correct.
(y-sin(x))dx=-tan(x)dy
So, $\frac{dy}{dx}=cos(x)-ycot(x) \newline$. This is an LDE with integrating factor $e^{\int{cot(x)dx}}=sin(x)$. Now, $y \cdot sin(x)=\int{sin(x)cos(x)}dx$

[dull stream]

SirLancelotDuLac