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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))

Respuesta :

Hagrid
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 be

square root (1 + x^2)

then
sin(tan−1(x)) = x / (square root (1 + x^2))

that being opposite over hypotenuse
and by the same triangle

cos(tan−1(x)) = x / (square root (1 + x^2))


CharlieStryker
Write the expression sin(tan^-1)x) as an algebraic expression in x (without trig or inverse trig functions).

Answer: if you were to write the expression shown above as an algebraic equation in x without using trig or inverse trig functions then the correct answer choice would be letter D) D. (x) / (sqrt (1+x^2)).

I hope it helps, Regards.

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