cos inverse (x2-y2/x2+y2)=tan inverse a prove that dy/dx =y/x pls do it wid componendo dividendo nd - Maths - Continuity and Differentiability

Question

cos inverse
(x2-y2/x2+y2)=tan
inverse a prove that dy/dx =y/x pls do it wid componendo dividendo
nd wat is compodendo and dividendo pls explain

Manmeet Singh · Accepted Answer

Say there is an expression $\frac{x}{y}$

By componendo and dividendo, we mean,

$\frac{x + y}{x - y}$

$\cos^{- 1} (\frac{x^{2} - y^{2}}{x^{2} + y^{2}}) = \tan^{- 1} a \Rightarrow \frac{x^{2} - y^{2}}{x^{2} + y^{2}} = \cos (\tan^{- 1} a) = P A p p l y i n g c o m p o n e n d o a n d d i v i d e n d o, \frac{2 x^{2}}{- 2 y^{2}} = \frac{P + 1}{P - 1} \Rightarrow \frac{x^{2}}{y^{2}} = \frac{1 + P}{1 - P} D i f f e r e n t i a t e b o t h s i d e s w . r . t x, \frac{y^{2} \frac{ⅆ}{ⅆ x} (x^{2}) - x^{2} \frac{ⅆ}{ⅆ y} (y^{2})}{(y^{2})^{2}} = 0 \Rightarrow 2 x y^{2} - 2 y x^{2} \frac{d y}{d x} = 0 \Rightarrow 2 x y^{2} = 2 y x^{2} \frac{d y}{d x} \Rightarrow y d x = x d y \Rightarrow \frac{d y}{d x} = \frac{y}{x} H e n c e p r o v e d .$

cos inverse (x2-y2/x2+y2)=tan inverse a prove that dy/dx =y/x pls do it wid componendo dividendo ....nd wat is compodendo and dividendo pls explain

cos inverse (x²-y²/x²+y²)=tan inverse a prove that dy/dx =y/x pls do it wid componendo dividendo ....nd wat is compodendo and dividendo pls explain