JEE Class main Answered

110

Asked by ssn | 09 Jun, 2022, 07:31: AM

Expert Answer

r₂ = 4 R sin(B/2) cos(C/2) cos(A/2)

r₃ = 4 R sin(C/2) cos(A/2) cos(B/2)

begin mathsize 14px style fraction numerator r subscript 2 plus r subscript 3 over denominator R end fraction space equals space 4 space open parentheses sin B over 2 cos C over 2 space plus space sin C over 2 cos B over 2 space close parentheses space cos A over 2 end style

begin mathsize 14px style fraction numerator r subscript 2 plus r subscript 3 over denominator R end fraction space equals space 4 space sin open parentheses fraction numerator B plus C over denominator 2 end fraction close parentheses space cos A over 2 space equals space 4 space cross times fraction numerator 1 over denominator square root of 2 end fraction cross times fraction numerator 1 over denominator square root of 2 end fraction space equals space 2 end style

begin mathsize 14px style space open parentheses because space space angle A space equals angle B space plus space angle C space equals space pi over 2 close parentheses end style

begin mathsize 14px style fraction numerator R over denominator r subscript 2 plus r subscript 3 end fraction space equals space 1 half end style

begin mathsize 14px style cos to the power of negative 1 end exponent open parentheses fraction numerator R over denominator r subscript 2 plus r subscript 3 end fraction close parentheses space equals space cos to the power of negative 1 end exponent space open parentheses 1 half close parentheses space equals space pi over 3 end style

Answered by Thiyagarajan K | 12 Jun, 2022, 13:11: PM

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