Question

If
$\sqrt{1 - {x}^{2} } + \sqrt{1 - {y}^{2} } is \: a(x - y) \: then \: show \: that \: dy \div d = \sqrt{?}$
​

Answer 1

Answer:

dy/dx = √ { ( 1-y²) / ( 1 - x²) }

Step-by-step explanation:

I think question is like this,

If, √(1 - x² ) + √( 1 - y² ) = a ( x - y ) , show that,

dy/dx = √{ ( 1 - y² ) / ( 1 - x² ) }

Solution--->

(1) plzzz refer the attachement

(2) First we substitute

x = Sinα and y = Sinβ

=> α = Sin⁻¹x and => β = Sin⁻¹ y

(3) Then we apply two trgonometrical formulee

CosC + CosD = 2 Cos( C + D / 2 ) Cos ( C-D / 2 )

SinC - SinD = 2 Cos ( C+ D / 2 ) Sin ( C - D / 2 )

(4) Then applying

Cotθ = Cosθ / Sinθ

(5) Then we put

α = Sin⁻¹x and β = Sin⁻¹y

(6) Differentiating with respet to x , and using

d / dx ( Sin⁻¹ x ) = 1 / √( 1 - x² )