Match the following. List – I List – II (A) Let y x = cos ⁡ 3 cos - 1 ⁡ x , x ϵ - 1 , 1 , x ≠ ± 3 2 . Then 1 y x x 2 - 1 d 2 y x d x 2 + x d y x d x equals (P) 1 (B) Let A 1 , A 2 , … , A n n > 2 be the vertices of a regular polygon of n sides with its centre at the origin. Let a k → be the position vector of the point A k , k = 1 , 2 , … n . If ∑ k

Step-by-step solution

P y = cos ⁡ 3 cos - 1 ⁡ x y ′ = 3 sin ⁡ 3 cos - 1 ⁡ x 1 - x 2 1 - x 2 y ′ = 3 sin ⁡ 3 cos - 1 ⁡ x ⇒ - x 1 - x 2 y ′ + 1 - x 2 y " = 3 c o s ⁡ ( 3 c o s - 1 x ) . - 3 1 - x 2 ⇒ - x y ′ + 1 - x 2 y " = - 9 y ⇒ 1 y [ x 2 - 1 y " + x y ′ ] = 9 Q a k × a k + 1 = r 2 sin ⁡ 2 π n a k . a k + 1 = r 2 cos ⁡ 2 π n ⇒ ∑ k = 1 n - 1 a k → × a k + 1 → = ∑ k = 1 n - 1 a k . a k + 1 ⇒ r 2 n - 1 sin ⁡ 2 π n = r 2 n - 1 cos ⁡ 2 π n tan ⁡ 2 π n = 1 ⇒ n = 8 4 k + 1 ⇒ n = 8 R h 2 6 + 1 2 3 = 1 , h = ± 2 Tangent at (2, 1) is 2 x 6 + y 3