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tan ( x+y) = a+b , tan (x-y ) = a-b , then show a tanx - b tany= a^2 - b^2 .

tan ( x+y) = a+b , tan (x-y ) = a-b , then show a tanx - b tany= a^2 - b^2 . 
 

Grade:11

1 Answers

vsujji
17 Points
8 years ago
[a+b][a-b]=tan[x+y].tan[x-y]
a^2-b^2=[tan^2x-tan^2y]/1-tan^2xtan62y].......................................................equation 1
         tan[x+y]+tan[x-y]=2a   
 …......we get    2a = [2tanx+2tanxtan^2y]/[1-tan^2xtan^2 y]
 
                         atanx=[tan^2x+tan^2xtan^2y]/[1-tan^2xtan^2y]
similarly  btany = [tan^2y+tan^2xtan^2y]/[1-tan^2xtan^y]
      atanx-btany = [tan^2x-tan^2y]/[1-tan^2xtan^2y]..........................................equation 2
from equation 1 and 2 weget  atanx-btany=a^2-b^2
 
 

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