Write the following in the simplest form :  from Mathematics I
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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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    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

    Put x = sec θ


    therefore space space space space 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 equals cot to the power of negative 1 end exponent open parentheses fraction numerator 1 over denominator square root of sec squared space straight theta minus 1 end root end fraction close parentheses equals cot to the power of negative 1 end exponent open parentheses fraction numerator 1 over denominator tan space straight theta end fraction close parentheses 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 space equals space cot to the power of negative 1 end exponent left parenthesis cot space straight theta right parenthesis equals straight theta equals sec to the power of negative 1 end exponent straight x therefore space space space 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 equals sec to the power of negative 1 end exponent straight x
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    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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    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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    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
    118 Views
    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
    112 Views
    Answer
    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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