Simplify from Mathematics Inverse Trigonometric Functions
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    Inverse Trigonometric Functions

    Multiple Choice QuestionsShort Answer Type

    81.

    Write tan to the power of negative 1 end exponent open parentheses fraction numerator 1 over denominator square root of straight x squared minus 1 end root end fraction close parentheses comma space open vertical bar straight x close vertical bar space greater than space 1 in the simplest form.

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    82.

    Write tan to the power of negative 1 end exponent open square brackets fraction numerator 3 straight a squared space straight x minus straight x cubed over denominator straight a left parenthesis straight a cubed minus 3 straight x squared right parenthesis end fraction close square brackets comma space straight a greater than 0 comma space space minus fraction numerator straight a over denominator square root of 3 end fraction less or equal than straight x less or equal than fraction numerator straight a over denominator square root of 3 end fraction in the simplest form.

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    Answer
    83. Write the following in the simplest form : 

    cot to the power of negative 1 end exponent open parentheses fraction numerator 1 over denominator square root of straight x squared minus 1 end root end fraction close parentheses comma space open vertical bar straight x close vertical bar greater than 1
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    Answer
    84. Write the following in the simplest form :tan to the power of negative 1 end exponent open parentheses fraction numerator straight x over denominator square root of straight a squared minus straight x squared end root end fraction close parentheses comma space open vertical bar straight x close vertical bar less than straight a
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    85. Write the following in the simplest form :

    tan to the power of negative 1 end exponent open square brackets square root of fraction numerator 1 minus cos space straight x over denominator 1 plus sin space straight x end fraction end root close square brackets
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    86. 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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    Answer
    87. Simplify

    cos to the power of negative 1 end exponent open square brackets square root of fraction numerator 1 plus cos space 3 x over denominator 1 minus cos space 3 x end fraction end root close square brackets
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    Answer
    88. Simplify

    tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 1 plus x squared end root minus 1 over denominator x end fraction close parentheses
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    Answer
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    89. Simplify

    tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 1 plus x squared end root minus 1 over denominator x end fraction close parentheses

    Let space straight z equals bold tan to the power of bold minus bold 1 end exponent open parentheses fraction numerator square root of bold 1 bold plus bold x to the power of bold 2 end root bold minus bold 1 over denominator bold x end fraction close parentheses Put space space space space space space space straight x equals tan space straight theta therefore space space space space space space straight z equals tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 1 plus tan squared space straight theta minus 1 end root over denominator tan space straight theta end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator sec space straight theta minus 1 over denominator tan space straight theta end fraction close parentheses equals tan to the power of negative 1 end exponent open square brackets fraction numerator begin display style fraction numerator 1 over denominator cos space straight theta end fraction end style minus 1 over denominator begin display style fraction numerator sin space straight theta over denominator cos space straight theta end fraction end style end fraction close square brackets space space space space space space space space space space equals space tan to the power of negative 1 end exponent open parentheses fraction numerator 1 minus cos space straight theta over denominator sin space straight theta end fraction close parentheses equals tan to the power of negative 1 end exponent open square brackets fraction numerator 2 space sin squared space begin display style straight theta over 2 end style over denominator 2 space sin space begin display style straight theta over 2 end style space cos space begin display style straight theta over 2 end style end fraction close square brackets space space space space space space space space space space equals tan to the power of negative 1 end exponent open parentheses tan straight theta over 2 close parentheses equals straight theta over 2 equals 1 half tan to the power of negative 1 end exponent space straight x
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    90. Simplify

    cot to the power of negative 1 end exponent open parentheses square root of 1 plus straight x squared end root minus straight x close parentheses
    144 Views
    Answer
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