Write  in the simplest form. from Mathematics Inverse Trigono

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

 Multiple Choice QuestionsShort Answer Type

Advertisement

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.


Let space straight x equals 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
Put space straight x space equals space sec space straight theta
therefore space straight z space equals space tan to the power of negative 1 end exponent equals open parentheses fraction numerator 1 over denominator square root of straight x squared minus 1 end root end fraction close parentheses equals tan 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
space space space space space space equals space tan to the power of negative 1 end exponent open parentheses fraction numerator 1 over denominator tan space straight theta end fraction close parentheses equals tan to the power of negative 1 end exponent space left parenthesis cot space straight theta right parenthesis equals tan to the power of negative 1 end exponent open square brackets tan open parentheses straight x over 2 minus straight theta close parentheses close square brackets
space space space space space space equals space straight pi over 2 minus sec to the power of negative 1 end exponent straight x
146 Views

Advertisement
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.

130 Views

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

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

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

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

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

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

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

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

Advertisement