If A+B+C =180, then find the minimum value of cot^2(A)+cot^2(B)+cot^2(C).

Question

Sunil Raikwar · Answer

We knoe that for positive integers AM greater than equal to GM cot 2 A+cot 2 B/2greater than equal to square root of (cot 2 Acot 2 B) cot 2 A+cot 2 B greater than equal to 2cotAcotB.............1 cot 2 B+cot 2 Cgreater than equal to 2cotBcotC............2 cot 2 A+cot 2 Cgreater than equal to 2cotAcotC.............3 adding eq. 1, 2 & 3 cot 2 A+cot 2 B+cot 2 c greater than equal to 2(cotAcotB+cotBcotC+cotCcotA) if A+B+C=180 then cotAcotB+cotBcotC+cotCcotA=1 cot 2 A+cot 2 B+cot 2 cgreater than equal to 2 Thanks & Regards Sunil Raikwar askIITians Faculty

Jaikarthik Suresh · Answer

We knoe that for positive integersAM greater than equal to GMcot2A+cot2B/2greater than equal to square root of (cot2Acot2B)cot2A+cot2B greater than equal to 2cotAcotB.............1cot2B+cot2Cgreater than equal to 2cotBcotC............2cot2A+cot2Cgreater than equal to 2cotAcotC.............3adding eq. 1, 2 & 32(cot2A+cot2B+cot2c) greater than equal to 2(cotAcotB+cotBcotC+cotCcotA)if A+B+C=180then cotAcotB+cotBcotC+cotCcotA=1cot2A+cot2B+cot2cgreater than equal to 1

Shrey Patel · Answer

We know that for positive integers AM greater than equal to GMcot2A+cot2B/2 greater than equal to square root of (cot2Acot2B)cot2A+cot2B greater than equal to 2cotAcotB.............1cot2B+cot2C greater than equal to 2cotBcotC............2cot2A+cot2C greater than equal to 2cotAcotC.............3adding eq. 1, 2 & 3cot2A+cot2B+cot2c greater than equal to cotAcotB+cotBcotC+cotCcotAif A+B+C=180then cotAcotB+cotBcotC+cotCcotA=1cot2A+cot2B+cot2c greater than equal to 1Hence, answer is 1.

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If A+B+C =180, then find the minimum value of cot^2(A)+cot^2(B)+cot^2(C).

If A+B+C =180, then find the minimum value of cot^2(A)+cot^2(B)+cot^2(C).

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