If y= ( sin^-1 ⁡x )^2+ ( cos^-1 ⁡x )^2, then (1-x^2)y_2-xy_1=

Question

Accepted Answer

Correct answer: B. (b) : y= ( sin^-1 ⁡x )^2+ ( cos^-1 ⁡x )^2 (i) On differentiating w.r.t. ' x ', we get y_1= 2 sin^-1 ⁡x 1-x^2- 2 cos^-1 ⁡x 1-x^2 \# ( ii ) Again, differentiating w.r.t. ' x ' we get = 2 1-x^2 1-x^2- 12 1-x^2 (-2x )2 sin^-1 ⁡x(1-x^2) -( -2 1-x^2 1-x^2+ 12 1-x^2 (2x )2 cos^-1 ⁡x)1-x^2 ⇒y^2 2+ 2x sin^-1 ⁡x 1-x^2+2- 2x cos^-1 ⁡x 1-x^21-x^2 ⇒(1-x^2)y_2=4+x( 2 sin^-1 ⁡x 1-x^2- 2 cos^-1 ⁡x 1-x^2) ⇒(1-x^2)y_2=4+xy_1 [Using (ii)] ⇒(1-x^2)y_2-xy_1=4

$If y = (sin^{- 1} x)^{2} + (cos^{- 1} x)^{2}, then (1 - x^{2}) y_{2} - x y_{1} =$

Solution

More Continuity & Differentiability PYQs