If √1-x2n+√1-y2n=a(xn-yn), then √(1-x2n/1-y2n) (dy/dx) is equal to

Question

If √1-x2n+√1-y2n=a(xn-yn), then √(1-x2n/1-y2n) (dy/dx) is equal to (A) 1 (B) x/y (C) (xn-1/yn-1) (D) None of these

Tardigrade Admin · Accepted Answer

Put xn=cos α, yn=cos β ⇒ a=(sin α+sin β/cos α-cos β)=(2 sin((α+β/2))cos((α-β/2))/-2 sin((α +β )2)sin((α -β )2) =-cot((α -β /2)) ⇒ 2 cot/-1)(-a)=α-β ⇒ cos-1(xn)-cos-1(yn)=2 cot-1(-a) ⇒ (yn-1/√1-y2n) (dy/dx)=(xn-1/√1-x2n) ⇒ √(1-x2x/1-y2n) (dy/dx)=(xn-1/yn-1)

Q. If $1 - x^{2 n} + 1 - y^{2 n} = a (x^{n} - y^{n})$ , then $\frac{1 - x ^{2 n}}{1 - y ^{2 n}} \frac{d y}{d x}$ is equal to

$1$

$x / y$

$\frac{x ^{n - 1}}{y ^{n - 1}}$

None of these

Q. If 1−x2n​+1−y2n​=a(xn−yn), then 1−y2n1−x2n​​dxdy​ is equal to

1

x/y

yn−1xn−1​

None of these

Q. If $1 - x^{2 n} + 1 - y^{2 n} = a (x^{n} - y^{n})$ , then $\frac{1 - x ^{2 n}}{1 - y ^{2 n}} \frac{d y}{d x}$ is equal to

$1$

$x / y$

$\frac{x ^{n - 1}}{y ^{n - 1}}$