InterviewSolution
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InterviewSolution
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If in a triangle ABC, `(1 + cos A)/(a) + (1 + cos B)/(b) + (1+ cos C)/(c) = (k^(2) (1 + cos A) (1 + cos B) (1 + cos C))/(abc)`, then k is equal toA. `(1)/(2 sqrt2R)`B. 2RC. `(1)/(R)`D. none of these |
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Answer» Correct Answer - B `L.H.S. = (1 + cos A)/(a) + (1 + cos B)/(b) + (1 + cos C)/(c)` `= (2 cos^(2).(A)/(2))/(2R sin A) + (2 cos^(2).(B)/(2))/(2R sin B) + (2 cos^(2).(C)/(2))/(2R sin C)` `= (1)/(2R) (cot.(A)/(2) + cot.(B)/(2) + cot.(C)/(2))` Now, `(1 + cos A)/(a) .(1 + cos B)/(b) .(1 + cos C)/(c)` `= (cos^(2).(A)/(2))/(R sin A).(cos^(2).(B)/(2))/(R sin B) .(cos^(2)/(C)/(2))/(R sin C)` `= (1)/(8R^(3)) cot.(A)/(2) cot.(B)/(2) cot.(C)/(2)` |
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