Write  in the simplest form. from Mathematics Inverse Trigono
    • Zigya Logo

    Previous Year Papers

    Download Solved Question Papers Free for Offline Practice and view Solutions Online.

    Test Series

    Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

    Test Yourself

    Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
    Advertisement

    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.

    146 Views
    Answer
    Advertisement
    Zigya App

    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.

    Let space space straight theta equals 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 squared minus 3 straight x squared right parenthesis end fraction close square brackets equals tan open square brackets fraction numerator 3 begin display style straight x over straight a end style minus begin display style straight x cubed over straight a cubed end style over denominator 1 minus begin display style fraction numerator 3 space straight x squared over denominator straight a squared end fraction end style end fraction close square brackets
                                                                        ( Dividing num. and deno by a3)
    Put  straight x over straight a equals tan space a
    therefore space space space space space space space space space space space space straight theta equals tan to the power of negative 1 end exponent open square brackets fraction numerator 3 space tan space straight a space minus space tan cubed space straight a over denominator 1 minus 3 space tan squared space straight a end fraction close square brackets equals tan to the power of negative 1 end exponent space left parenthesis tan space 3 straight a right parenthesis space equals space 3 space straight a therefore space space space space space space space space space space space space straight theta space equals space 3 space tan to the power of negative 1 end exponent space straight x over straight a
    130 Views
  • Switch Icon Switch
    • Advertisement
    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
    131 Views
    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
    106 Views
    Answer
    Advertisement
    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
    135 Views
    Answer
    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
    117 Views
    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
    101 Views
    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
    118 Views
    Answer
    Advertisement
    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
    Advertisement
    Flag Popup Icon
    Flag it
    Submit
    Flag Popup Icon
    Switch to
    flexipad
    Share It Icon
    Share it
    Share It
    Share it