sinx-cosx=-2/5?

Question

Given: sinx-cosx=-2/5
Find: sin(2x)
tan(2x)
i found sin2x as 21/25
i can't seem to get tan2x

Answer 1

sin x - cos x = -2/5
(sin x - cos x)² = 4/25
sin²x - 2(sin x)(cos x) + cos²x = 4/25
(sin²x + cos²x) - 2(sin x)(cos x) = 4/25
1 - sin(2x) = 4/25
sin(2x) = 1 - 4/25 = 21/25

cos²(2x) = 1 - sin²(2x) = 1 - (21/25)² = 184/625
cos(2x) = (√184)/25

tan(2x) = sin(2x)/cos(2x) = (21/25)/[(√184)/25] = 21/√184

Answer 2

How about a hint?

tan(2x) = sin(2x) / cos(2x)

You already know sin(2x) and you should know cos(2x)