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

Question

csc(u) = 5,    0 < u < 𝜋/2

sin(2u) =

cos(2u) =

tan(2u) =

Answer 1

cscu = 5, sinu = 1/5

cos(2u) = 1 - 2sin²u = 1 - 2/25 = 23/25;

sin(2u) = 2sinucosu = 2·1/5·√1 - 1/25 = 2/5·2√6/5 = 4√6/25;tan(2u) = sin(2u)/cos(2u) = (4√6/25)/(23/25) = 4√6/23

Answer 2

csc u = 5 ⇒ sin u = 1/5

sin u = 1/5 ⇒ cos u √3/2

Now substitute values in appropriate formula.