Statement-1: If the angle between two asymptotes  of a hyperbola  x2a2−y2b2=1 is π3 its eccentricity is 23.Statement 2: Angles between the asymptotes of the hyperbola x2a2−y2b2=1 are 2tan−1⁡ba or  π−2tan−1⁡ba.

Equation of the asymptotes is xa±yb=0And if θ is an angle between the asymptotes tan θ =2ba1+b2a2=2tan⁡ϕ1+tan2⁡ϕ where ϕ=tan−1⁡ba=tan⁡2ϕ⇒θ=2ϕ=2tan−1⁡ba and the statement-1 is true. Using in statement-1. If π3=2tan−1⁡ba⇒tan⁡π6=ba⇒3b2=a2⇒3e2−1=1⇒e=23 If π3=π−2tan−1⁡ba⇒ba=tan⁡π3=3⇒b2=3a2⇒e2−1=3⇒e=2Showing that statement-1 is false