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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

(i) sin (sin^–1x + cos^–1.x) = $sin space straight pi over 2 equals 1$

$left parenthesis ii right parenthesis space straight L. space straight H. space straight S. italic space equals space cos left parenthesis sec to the power of negative 1 end exponent space straight x space plus space cosec to the power of negative 1 end exponent straight x right parenthesis equals cos space straight pi over 2 space space space space space space space space space space space space space space space space space space space equals 0 equals straight R. straight H. straight S. therefore space space space space space space space space straight L. straight H. straight S. space space space equals space straight R. space straight H. space straight S. space$