plzz explain how to solve it with the solution

Asked by ABHILASHA | 7th Sep, 2019, 03:14: PM

Expert Answer:

fraction numerator x minus y over denominator x plus y end fraction equals fraction numerator cos begin display style alpha end style begin display style plus end style begin display style i end style begin display style sin end style begin display style alpha end style begin display style minus end style begin display style open parentheses cos beta plus i sin beta close parentheses end style over denominator begin display style cos end style begin display style alpha end style begin display style plus end style begin display style i end style begin display style sin end style begin display style alpha end style begin display style plus end style cos begin display style beta end style begin display style plus end style begin display style i end style begin display style sin end style begin display style beta end style end fraction
equals fraction numerator begin display style cos alpha minus cos beta plus i left parenthesis sin alpha minus sin beta right parenthesis end style over denominator begin display style cos alpha plus cos beta plus i left parenthesis sin alpha plus sin beta right parenthesis end style end fraction
equals fraction numerator negative 2 sin open parentheses begin display style fraction numerator alpha plus beta over denominator 2 end fraction end style close parentheses sin open parentheses begin display style fraction numerator alpha minus beta over denominator 2 end fraction end style close parentheses plus 2 i cos open parentheses begin display style fraction numerator alpha plus beta over denominator 2 end fraction end style close parentheses sin open parentheses begin display style fraction numerator alpha minus beta over denominator 2 end fraction end style close parentheses over denominator 2 cos open parentheses begin display style fraction numerator alpha plus beta over denominator 2 end fraction end style close parentheses cos open parentheses begin display style fraction numerator alpha minus beta over denominator 2 end fraction end style close parentheses plus 2 i sin open parentheses begin display style fraction numerator alpha plus beta over denominator 2 end fraction end style close parentheses cos open parentheses begin display style fraction numerator alpha minus beta over denominator 2 end fraction end style close parentheses end fraction
equals fraction numerator sin begin display style open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses end style begin display style open parentheses negative sin open parentheses fraction numerator begin display style alpha plus beta end style over denominator 2 end fraction close parentheses plus i cos open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses close parentheses end style over denominator cos begin display style open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses end style begin display style open parentheses cos open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses plus i sin open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses close parentheses end style end fraction
equals fraction numerator begin display style sin open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses open parentheses negative sin open parentheses fraction numerator begin display style alpha plus beta end style over denominator 2 end fraction close parentheses plus i cos open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses close parentheses end style over denominator cos begin display style open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses cross times i over i cross times end style begin display style open parentheses cos open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses plus i sin open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses close parentheses end style end fraction
equals fraction numerator begin display style sin open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses open parentheses negative sin open parentheses fraction numerator begin display style alpha plus beta end style over denominator 2 end fraction close parentheses plus i cos open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses close parentheses end style over denominator begin display style 1 over i end style begin display style cross times end style cos begin display style open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses end style begin display style open parentheses i cos open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses minus sin open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses close parentheses end style end fraction
equals i tan open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses
H e n c e comma space fraction numerator begin display style x minus y end style over denominator begin display style x plus y end style end fraction equals i tan open parentheses fraction numerator begin display style alpha minus beta end style over denominator begin display style 2 end style end fraction close parentheses

Answered by Renu Varma | 9th Sep, 2019, 10:55: AM