The general solution of sinx-cosx=2, for any integern is
nπ
2nπ+3π4
2nπ
(2n+1)π
Find the general solution
Given, sinx-cosx=2
Dividing by 2 on both sides,
⇒12sinx-12cosx=1⇒sinπ4sinx-cosπ4cosx=1∵sinπ4=12,cosπ4=12⇒-cosx+π4=1∵cosAcosB-sinAsinB=cosA+B⇒cosx+π4=-1⇒cosx+π4=cosπ
Therefore, x+π4=2nπ+π
⇒x=2nπ+π-π4⇒x=2nπ+3π4
Hence, option (B) is the correct answer.