In a triangle A B C , if cot A 2 cot B 2 = K , then all the possible values of K lies in

Question

In a triangle A B C , if cot A 2 cot B 2 = K , then all the possible values of K lies in, ( 0 , 1 ], [ 1 , ∞ ), ( 1 , ∞ ), ( 0 , 1 )

MARKS App · Accepted Answer

cot A 2 cot B 2 = K ⇒ r r - a r - b r - c . r r - b r - a r - c = K ⇒ r r - c = K ⇐ r - c + c r - c = K ⇒ 1 + c r - c = K . . . . . i Let p = c r - c = 2 c a + b - c a + b > c ⇒ p > 0 ∙ If angle C approaches 180 ° , then a + b - c → 0 + , p → + ∞ So, K ∈ 1 , ∞

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