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## Question

Write the expression sin(tan^-1)x) as an algebraic expression in x (without trig or inverse trig functions). A. (sqrt (1+x^2))/ (x). B. (1) / (sqrt (1+x^2)). C. (x) / (sqrt (1-x^2)). D. (x) / (sqrt (1+x^2)). E. (1) / (sqrt (1-x^2))

## Answer

The correct answer for this question is letter “D. (x) / (sqrt (1+x^2)).”Make a triangle. yes a triangle. label “opposite” side x and adjacent side 1 since the tangent is x = x/1 use pythatoras to find the hypotenuse which will besquare root (1 + x^2)thensin(tan−1(x)) = x / (square root (1 + x^2))that being opposite over hypotenuseand by the same trianglecos(tan−1(x)) = x / (square root (1 + x^2))

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