If a>b>c>0, Prove that 

Cot^-1 [(ab+1)÷(a-b)]+ Cot^-1 [(bc+1)÷(b-c)]+Cot^-1[(ca+1)÷(c-a)]= pi 

Asked by mridulabarua05 | 21st Feb, 2019, 01:05: PM

Expert Answer:

begin mathsize 16px style cot to the power of negative 1 end exponent open parentheses fraction numerator ab plus 1 over denominator straight a minus straight b end fraction close parentheses plus cot to the power of negative 1 end exponent open parentheses fraction numerator bc plus 1 over denominator straight b minus straight c end fraction close parentheses plus cot to the power of negative 1 end exponent open parentheses fraction numerator ca plus 1 over denominator straight c minus straight a end fraction close parentheses
equals tan to the power of negative 1 end exponent open parentheses fraction numerator straight a minus straight b over denominator 1 plus ab end fraction close parentheses plus tan to the power of negative 1 end exponent open parentheses fraction numerator straight b minus straight c over denominator 1 plus bc end fraction close parentheses plus tan to the power of negative 1 end exponent open parentheses fraction numerator straight c minus straight a over denominator 1 plus ca end fraction close parentheses
equals tan to the power of negative 1 end exponent straight a minus tan to the power of negative 1 end exponent straight b plus tan to the power of negative 1 end exponent straight b minus tan to the power of negative 1 end exponent straight c plus tan to the power of negative 1 end exponent straight c minus tan to the power of negative 1 end exponent straight a
equals 0 end style
 
 
 
 
 
 
 
NOTE: Please check RHS side of the question.

Answered by Sneha shidid | 21st Feb, 2019, 02:39: PM