Simplify the following expressions. Your answer cannot contain any trig function

Question

Simplify the following expressions.

  Your answer cannot contain any trig functions.

Simplify the following expressions.

  Your answer cannot contain any trig functions.

Evaluate the following expressions. Your answer cannot contain any trig functions.

Simplify the following expressions. sin(tan-1 (x/5)) = sin(2 tan-1 (x/5)) = Your answer cannot contain any trig functions. Simplify the following expressions. cos(tan-1 (x/3)) = cos(2tan-1 (x/3)) = Your answer cannot contain any trig functions. Evaluate the following expressions. Your answer cannot contain any trig functions. sin(cos-1 (3/2)) = tan(cos-1 (1)) =

Explanation / Answer

sin(tan^-1(x/5) ) = sin(sin^-1(x/sqrt(x^2 + 25)) = x/sqrt(x^2 + 25)

sin(2tan^-1(x/5)) = 2*sin(tan^-1(x/5)) *cos(tan^-1(x/5)) = 2*x/sqrt[x^2 + 25] * 5/sqrt[x^2 +25] = 10x/[x^2 + 25]

cos(tan^-1(x/3)) = cos(cos^-1(3/sqrt(x^2 + 9)) = 3/sqrt(x^2 + 9)

cos(2tan^-1(x/3)) = 2cos(tan^-1(x/3)) - 1 = 2*3/sqrt(x^2 + 9) - 2 = 6/sqrt(x^2 + 9) - 2

sin(cos^-1(sqrt(3)/2)) = sin(sin^-1(1/2)) = 1/2

tan(cos^-1(1)) = 0

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