Question

answer this question please​

Answer 1

${\huge{\underline{\textbf{\textsf{\color{navy}{An}}{\purple{sw}}{\pink{er}}}}}}$

$we \: \: have \: \: \\ {tan}^{ - 1} ( \frac{acosx - bsinx}{bcosx + asinx} ) \\ = {tan}^{ - 1} ( \frac{ \frac{acosx - bsinx}{bcosx} }{ \frac{bcosx + asinx}{bcosx} } ) \\ = {tan}^{ - 1} ( \frac{ \frac{a}{b} - tanx }{1 + \frac{a}{b} tanx} ) \\ = {tan}^{ - 1} \frac{a}{b} - {tan}^{ - 1} (tanx) \\ = {tan}^{ - 1} \frac{a}{b} - x$