Inverse Trigonometric Functions

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Write the following in the simplest form : - Wired Faculty

Question

Write the following in the simplest form :

$tan to the power of negative 1 end exponent open parentheses fraction numerator cos space straight x minus sin space straight x over denominator cos space straight x plus sin space straight x end fraction close parentheses$

Solution

tan to the power of negative 1 end exponent open parentheses fraction numerator cos space straight x minus sin space straight x over denominator cos space straight x plus sin space straight x end fraction close parentheses equals tan to the power of negative 1 end exponent open square brackets fraction numerator begin display style fraction numerator cos space straight x over denominator cos space straight x end fraction end style minus begin display style fraction numerator sin space straight x over denominator bold cos bold space bold x end fraction end style over denominator begin display style fraction numerator cos space straight x over denominator cos space straight x end fraction end style plus begin display style fraction numerator sin space straight x over denominator cos space straight x end fraction end style end fraction close square brackets equals tan to the power of negative 1 end exponent open square brackets fraction numerator 1 minus tan space straight x over denominator 1 plus tan space straight x end fraction close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space tan to the power of negative 1 end exponent open square brackets tan open parentheses straight pi over 4 minus straight x close parentheses close square brackets equals straight pi over 4 minus straight x therefore space space space space space space tan to the power of negative 1 end exponent open parentheses fraction numerator cos space straight x minus sin space straight x over denominator cos space straight x space plus sin space straight x end fraction close parentheses equals straight pi over 4 minus straight x

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Inverse Trigonometric Functions

Write the following in the simplest form :

$tan to the power of negative 1 end exponent open parentheses fraction numerator cos space straight x minus sin space straight x over denominator cos space straight x plus sin space straight x end fraction close parentheses$

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