Question

if cos y is equal to x cos (a + y) with cos a not equal to plus minus one, prove that dy/dx is equal to cos square (a + y) whole upon sin a i.e. dy/dx=(cos^2(a+y))/sin a

Answer 1

wELCOME TO OPENSTUDY
where u can ask questions and answer questions
and give medals and fan people that helped you so much that want to ask a question you just have to do this @utkarsh3598 to get them to your question!!!!

Answer 2

say hi or something so u can get your very first medal

Answer 3

hello?

Answer 4

\[
\begin{align*}
\cos(y)&=x\cos(a+y)\implies x=\frac{\cos(y)}{\cos(a+y)}\\
\frac{d}{dx}\cos(y)&=\frac{d}{dx}\left(x\cos(a+y)\right)\\
-\sin(y)\frac{dy}{dx}&=\cos(a+y)-x\sin(a+y)\frac{dy}{dx}\\
\frac{\cos(y)}{\cos(a+y)}\sin(a+y)\frac{dy}{dx}-\sin(y)&=\cos(a+y)\\
\frac{dy}{dx}\left(\sin(a+y)\cos(y)-\sin(y)\cos(a+y)\right)&=\cos^2(a+y)\\
\frac{dy}{dx}\sin(a)&=\cos^2(a+y)\\
\frac{dy}{dx}&=\frac{\cos^2(a+y)}{\sin(a)}
\end{align*}
\]

Answer 5

thank you thomas, in the 4th line(step) i think there should be dy/dx with sin(y). will you please explain it. after fourth step it is not clear.

Answer 6

Yes I missed dy/dx in the fourth line. Thanks for pointing that out.