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Inverse Trigonometric Functions

Short Answer Type

11. Find the values of each of the expressions

tan to the power of negative 1 end exponent open parentheses tan space fraction numerator 3 straight pi over denominator 4 end fraction close parentheses

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12. Using principle value, evaluate the following :

cos to the power of negative 1 end exponent open parentheses cos fraction numerator 2 straight pi over denominator 3 end fraction close parentheses plus sin to the power of negative 1 end exponent open parentheses sin fraction numerator 2 straight pi over denominator 3 end fraction close parentheses.

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13.

Find the value of each of the following :

(i) sin (sin^–1x + cos^–1.x) (ii) cos (sec^–1x + cosec^–1x). | x | ≥ 1

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14. Find the principal value of sin^–1 $open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses.$

$Let space space straight y space equals sin to the power of negative 1 end exponent open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses space where space space straight pi over 2 less or equal than space straight y space less or equal than space straight pi over 2 therefore space space space sin space straight y space equals fraction numerator 1 over denominator square root of 2 end fraction space where space minus straight pi over 2 space less or equal than space straight y space less or equal than space straight pi over 2 therefore space space space space space space space space straight y equals straight pi over 4 therefore space space space space space space space required space principal space value space equals space straight pi over 4$