CUET PG 2023 — Mathematics PYQ

Maan lete hain $x=\cot A\cot B$, $y=\cot B\cot C$, aur $z=\cot C\cot A$.

Identity ke hisaab se $x+y+z=1$.

AM-GM inequality ke anusar:

Values substitute karne par:

Step 2: K ki value find karna

Humein diya gaya hai $\cot A\cot B\cot C=K$. Toh upar wali equation ban jayegi:

Dono sides ka cube karne par:

Iska matlab hai:

Step 3: Maximum Value of K

$K$ ki maximum value tab hoti hai jab triangle equilateral ho ($A=B=C=60^{\circ }$):