question_answer

The general solution of \[a\,cos\,x\text{+}b\,sin\,x=c,\] where a, b, c are constants, will be.

A)  \[x=n\pi +{{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)\]

B)  \[x=2n\pi -{{\tan }^{-1}}(b/a)\]

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

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

E)  None of these