If acos θ = bcos (θ+120°) = c cos (θ+240°) , then find the value of 1/a+1/b+1/c

Asked by tps.mjmdr | 16th Jun, 2018, 05:45: PM

Expert Answer:

acos θ = bcos (θ+120°) = c cos (θ+240°) = k(say)
 
begin mathsize 16px style straight k over straight a equals cosθ comma space fraction numerator begin display style straight k end style over denominator begin display style straight b end style end fraction equals cos open parentheses straight theta plus 60 degree close parentheses comma fraction numerator begin display style straight k end style over denominator begin display style straight c end style end fraction equals cos open parentheses straight theta plus 240 degree close parentheses
Consider comma space
fraction numerator begin display style straight k end style over denominator begin display style straight a end style end fraction plus fraction numerator begin display style straight k end style over denominator begin display style straight b end style end fraction plus fraction numerator begin display style straight k end style over denominator begin display style straight c end style end fraction equals cosθ space plus space cos open parentheses straight theta plus 60 degree close parentheses space plus space cos open parentheses straight theta plus 240 degree close parentheses
space space space space space space space space space space space space space space space space space space space space space space equals 2 cos left parenthesis straight theta plus 60 degree right parenthesis cos left parenthesis 60 degree right parenthesis space plus space space cos open parentheses straight theta plus 240 degree close parentheses
space space space space space space space space space space space space space space space space space space space space space space equals 2 cos left parenthesis straight theta plus 60 degree right parenthesis fraction numerator begin display style 1 end style over denominator 2 end fraction space plus space space cos open parentheses straight theta plus 240 degree close parentheses
space space space space space space space space space space space space space space space space space space space space space space space equals space cos left parenthesis straight theta plus 60 degree right parenthesis space plus space space cos open parentheses straight theta plus 240 degree close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space equals space 2 cos open parentheses straight theta plus 150 degree close parentheses cos 90 degree
fraction numerator begin display style straight k end style over denominator begin display style straight a end style end fraction plus fraction numerator begin display style straight k end style over denominator begin display style straight b end style end fraction plus fraction numerator begin display style straight k end style over denominator begin display style straight c end style end fraction equals space 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space cos 90 degree equals 0
fraction numerator begin display style 1 end style over denominator begin display style straight a end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight b end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight c end style end fraction equals space 0 space
end style

Answered by Sneha shidid | 19th Jun, 2018, 11:27: AM