If ( 4 )= ( 4 ) , then the general solution of is

Step-by-step solution

The equation ( 4 ) = ( 4 ) is equivalent to ( 4 ) = ( 2 - 4 ) using the identity x = ( 2 - x ) . The general solution for A = B is A = n + (-1)^n B , where n Z . Applying this yields 4 = n + (-1)^n ( 2 - 4 ) . Dividing through by 4 gives = 4n + (-1)^n (2 - ) . Assuming the arguments of sine and cosine are acute angles, A = B implies A = 2 - B . Thus, 4 = 2 - 4 . Multiplying both sides by 4 yields = 2 - , which simplifies to + = 2 . Since + = 1 = 2 (2 ) , we obtain 2 (2 ) = 2 , hence (2 ) = 1 . The general solution