trig question (1 Viewer)

[SeftonIsAHole]

Ok heres the question.

ABC is an acute-angled triangle.
i)Show that: tan(A+B)=-tanC
ii)Hence, show that: tanA+tanB+tanC=tanA.tanB.tanC

EDIT: Nvm, i got it lol

For (i) A+B+C = 180 (angle sum of a triangle)
therefore A+B=180-C
tan(A+B)=tan(180-C)
tan(A+B)=-tanC

(ii) tan(A+B)=-tanC
(tanA+tanB)/(1-tanAtanB)=-tanC
tanA+tanB+tanC=tanAtanBtanC

 

[lyounamu]

Ok heres the question.

ABC is an acute-angled triangle.
i)Show that: tan(A+B)=-tanC
ii)Hence, show that: tanA+tanB+tanC=tanA.tanB.tanC

EDIT: Nvm, i got it lol

For (i) A+B+C = 180 (angle sum of a triangle)
therefore A+B=180-C
tan(A+B)=tan(180-C)
tan(A+B)=-tanC

(ii) tan(A+B)=-tanC
(tanA+tanB)/(1-tanAtanB)=-tanC
tanA+tanB+tanC=tanAtanBtanC

Well done~

 

[Timothy.Siu]

nice, i didn't get that

 

[ratcher0071]

nice, i didn't get that

I didn't get that too.

 

[lyounamu]

Don't you think it was as if he knew the question already and just wrote it out?

There is not even a sign of edition. But the question wasn't hard so that's another possibility.