Question 1172165
Find the exact values of  sin(2u), cos(2u), and tan(2u) using the double-angle formulas.

csc(u) = 6,   0 < u < 𝜋/2

sin(2u)	 = 	
 
cos(2u)	 = 	
 
tan(2u)	 =
<pre>With {{{0 < u < pi/2}}}, 0 is in the 1st quadrant
{{{matrix(2,7, csc (u), "=", H/O, "=", 6/1, "=", r/y, sin (u), "=", O/H, "=", y/r, "=", 1/6)}}}      {{{matrix(5,3, x^2, "=", r^2 - y^2, x^2, "=", 6^2 - 1^2, x^2, "=", 36 - 1, x^2, "=", 35, x, "=", sqrt(35))}}}
{{{matrix(1,7, cos (u), "=", A/H, "=", x/r, "=", sqrt(35)/6)}}}
{{{highlight_green(system(matrix(3,3, sin (2u), "=", 2 * sin (u) cos (u), sin (2u), "=", 2 * (1/6) * (sqrt(35)/6), sin (2u), "=", (1/3) * (sqrt(35)/6)), highlight(matrix(1,3, sin (2u), "=", sqrt(35)/18))))}}}    {{{highlight_green(system(matrix(4,3, cos (2u), "=", cos^2 (u) - sin^2 (u), 
cos (2u), "=", (sqrt(35)/6)^2 - (1/6)^2, cos (2u), "=", (35/36) - (1/36),
cos (2u), "=", 34/36), highlight(matrix(1,3, cos (2u), "=", 17/18))))}}}    {{{ highlight_green(system(matrix(4,3, tan (2u), "=", sin (2u)/cos (2u), tan (2u), "=", (sqrt(35)/18)/(17/18), tan (2u), "=", (sqrt(35)/18) * (18/17), tan (2u), "=", (sqrt(35)/cross(18)) * (cross(18)/17)), highlight(matrix(1,3, tan (2u), "=", sqrt(35)/17)))))}}}