sin(3a+b)+sin(3a-b)+sin(b-a)-sin(b+a)=cosb
solve the equation

Asked by Anil | 17th Jun, 2017, 08:10: PM

Expert Answer:

begin mathsize 16px style sin left parenthesis 3 straight a plus straight b right parenthesis plus sin left parenthesis 3 straight a minus straight b right parenthesis plus sin left parenthesis straight b minus straight a right parenthesis minus sin left parenthesis straight b plus straight a right parenthesis
equals sin 3 straight a space cosb plus up diagonal strike cos 3 straight a space sinb end strike space plus sin 3 straight a space cosb minus up diagonal strike cos 3 straight a space sinb space end strike
space space space space plus sinb space cosa minus cosb space sina minus open parentheses sinb space cosa plus cosb space sina close parentheses
equals 2 sin 3 straight a space cosb space plus up diagonal strike sinb space cosa end strike minus cosb space sina minus up diagonal strike sinb space cosa end strike minus cosb space sina
equals 2 sin 3 straight a space cosb minus 2 cosb space sina
equals 2 cosb open parentheses sin 3 straight a minus sina close parentheses
equals 2 cosb space open parentheses 2 cos open parentheses fraction numerator 3 straight a plus straight a over denominator 2 end fraction close parentheses sin open parentheses fraction numerator 3 straight a minus straight a over denominator 2 end fraction close parentheses close parentheses
equals 4 cosb space cos 2 straight a space sina
Please space check space the space RHS space of space the space question. end style

Answered by Sneha shidid | 19th Jun, 2017, 10:38: AM