若cos(3π−x)−3cos(x+π2)＝0，则tan(x+π4)等于（）A.−12B.-2C.12D.2

Question

若cos(3π−x)−3cos(x+(π)/(2))＝0，则tan(x+(π)/(4))等于（　　）
A. −(1)/(2)
B. -2
C. (1)/(2)
D. 2

Answer 1

∵cos（3π-x）-3cos（x+(π)/(2)）=-cosx+3sinx=0
∴3sinx=cosx
∴tanx=(1)/(3)
∴tan（x+(π)/(4)）=((1)/(3)+1)/(1−(1)/(3)×1)=2
故选：D．