If sinx cosx = 2/5 and tan x = 1/2, then sin^2x =

Question

If sinx cosx = 2/5 and tan x = 1/2, then sin² x=

A. 1/5 B. 2/5 C. sqrt(5)/5 D. 2sqrt(5)/5 E. 3/5

Answer 1

Since tanx = 1/2, sinx / cosx = 1/2. So, cosx = 2sinx

sinxcosx = 2/5

2sin²x = 2/5

sin²x = 1/5

sinx = 1 / √5 = √5 / 5