The general solution of \[a\cos x+b\sin x=c,\] where\[a,\,\,b,\,\,c\] are constants

• A. \[x=n\pi +{{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)\]
• B. \[x=2n\pi -{{\tan }^{-1}}\left( \frac{b}{a} \right)\]
• C. \[x=2n\pi -{{\tan }^{-1}}\left( \frac{b}{a} \right)\pm {{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)\]
• D. \[x=2n\pi +{{\tan }^{-1}}\left( \frac{b}{a} \right)\pm {{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)\]