Use the given information to find cos(2x), sin(2x), and tan(2x). (Enter your answers in exact form.) csc(x) = −2, 𝜋 < x < 3𝜋/2

Answer 1

sinx = -1/2; cos2x = 1 - 2sin²x = 1 - 2(- 1/2)² = 1/2; sin2x = 2sinxcosx, cosx = - √1 - 1/4 = - √3/2;

sin2x = 2(-1/2)(-√3/2) = √3/2; tan2x = sin2x/cos2x = - √3/2/(1/2) = - √3