Inverse Trigonometric Functions

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Question

Simplify $tan to the power of negative 1 end exponent open square brackets fraction numerator straight a space cos space straight x minus straight b space sin space straight x over denominator straight b space cos space straight x plus straight a space sin space straight x end fraction close square brackets comma space if space straight a over straight b space tan space straight x greater than negative 1.$

Solution

tan to the power of negative 1 end exponent open square brackets fraction numerator straight a space cos space straight x minus straight b space sin space straight x over denominator straight b space cos space straight x plus straight a space sin space straight x end fraction close square brackets equals tan to the power of negative 1 end exponent open square brackets fraction numerator begin display style fraction numerator straight a space cos space straight x minus straight b space sin space straight x over denominator straight b space cos space straight x end fraction end style over denominator begin display style fraction numerator straight b space cos space straight x plus straight a space sin space straight x over denominator straight b space cos space straight x end fraction end style end fraction close square brackets equals space tan to the power of negative 1 end exponent open square brackets fraction numerator begin display style straight a over straight b end style minus tan space straight x over denominator 1 plus begin display style straight a over straight b end style space tan space straight x end fraction close square brackets equals tan to the power of negative 1 end exponent straight a over straight b minus tan to the power of negative 1 end exponent left parenthesis tan space straight x right parenthesis equals tan to the power of negative 1 end exponent straight a over straight b minus straight x.