急! F4 Basic Trigonometry 1條數

Sincetanθ> 0 and sinθ < 0, then
θis in the 3rd quadrant, and cosθ < 0

tanθ =3
sinθ /cosθ = 3
sin²θ /cos²θ = 9
sin²θ = 9cos²θ ...... [1]

sin²θ+ cos²θ = 1 ...... [2]

Put [1] into [2] :
9cos²θ + cos²θ = 1
cos²θ= 1/10
cos²θ= 10/100
cosθ =-(√10)/10

Put cos²θ= 1/10 into [1] :
sin²θ= 9/10
sin²θ= 90/100
sinθ =-3(√10)/10

Hence, sinθ +cosθ
= -3(√10)/10- (√10)/10
= -4(√10)/10
= -2(√10)/5