" 33.If "y=((cos x-sin x))/((cos x+sin x))," prove that "(dy)/(dx)+y^(2)+1=0

Find (dy)/(dx) , when : If y=((cos x - sin x))/((cos x + sin x)) , prove that (dy)/(dx)+y^(2)+1=0 .

If y=sin^(-1)(cos x)+cos^(-1)(sin x) , prove that (dy)/(dx)=-2

If y=sin^(-1)(cos x)+cos^(-1)(sin x) , prove that (dy)/(dx)=-2

If y=(cos x-sin x)/(cos x+sin x) then ((d^(2)y)/(dx^(2)))/((dy)/(dx))=

if y = sqrt ((1 + sin x) / (1-sin x)), prove that cos x (dy) / (dx) = y

Ify,=sqrt(((1+cos x)/(2))), provethat (dy)/(dx)=-(1)/(2)(sin x)/(2) If y,=sqrt((1+sin x)/(1-sin x)), prove that cos x(dy)/(dx)=y

If y,=x sin y, prove that (dy)/(dx),=(sin y)/((1-x cos y))

If y,=x sin y, prove that (dy)/(dx),=(y)/(x(1-x cos y))

If y=sin x+cos x then (dy)/(dx) =

If y=sin(sin x), prove that (d^(2)y)/(dx^(2))+tan x(dy)/(dx)cos^(2)x=0