If m ( -30^ )=n ( +120^ ) , then m+n m-n =

Step-by-step solution

Given : m ( -30^ )= n ( +120) aligned & m ( -30^ )=- n ( +30) & n m =- ( -30) ( +30) aligned aligned & =- ( - 30 1+ 30 ) ( 30 1- 30 ) & = ^2 30- ^2 1- ^2 ^2 30 aligned Now, m+n m-n = 1+ n m 1- n m = 1+ ^2 30- ^2 1- ^2 ^2 30 1- ^2 30- ^2 1- ^2 ^2 30 aligned & = (1- ^2 ) (1+ ^2 30 ) (1+ ^2 ) (1- ^2 30 ) & = ( ^2 - ^2 ) ( ^2 30+ ^2 30 ) ( ^2 + ^2 ) ( ^2 30- ^2 30 ) & = 2 1 1 (2 60) = 2 1 2 aligned =2 2