Question

已知tanx=2，求2/3sinxcosx的值

Answer 1

tanx=2
即：sinx / cosx = 2
所以：sinx = 2cosx ，即：sin^2x = 4cos^2x
所以：sinx + cosx = 3cosx , sinx^2 + cosx^2 = 5cosx^2
所以：sin^2x + cos^2x + 2sinxcosx = 9cos^2x , cos^2x = 0.2
所以：2sinxcosx = 9cos^2x - 1 = 9*0.2 - 1 = 3.5
所以：2/3sinxcosx = 3.5/3 = 7/6

Answer 2

2/3sinxcosx
=2/3sinxcosx/(sin²x+cos²x)
=2/3tanx/(tan²x+1)——(分子分母同时除以cos²x)
=(2/3)×2/(4+1)
=(2/3)×2/5
=4/15