Evaluate sin[ tan^-1 (- 1) ]

Solution

sin[ tan^-1 (- 1) ] is a number lying between $straight pi over 2 space and space straight pi over 2$ [ by definition ]
and tan x = -1 when x = $negative straight pi over 4$
$therefore space space space space tan to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis space equals space minus straight pi over 4$
Now sin [ tan^-1 (- 1) = sin $open parentheses negative straight pi over 4 close parentheses equals negative fraction numerator 1 over denominator square root of 2 end fraction$

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Inverse Trigonometric Functions

Evaluate sin[ tan^-1 (- 1) ]

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Inverse Trigonometric Functions

Evaluate sin[ tan-1 (- 1) ]

Some More Questions From Inverse Trigonometric Functions Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Evaluate sin[ tan^-1 (- 1) ]