Basic trigonometry

Geometry Level 3

If $X+Y=0$ , which of the following statements is/are always true?

I and II only III only I and III only II only The three statements are always true I only None of the statements is always true II and III only

2 solutions

Parth Sankhe
Dec 18, 2018

sin and tan are odd functions, while cos is even

ابراهيم فقرا
Dec 18, 2018

$\sin(X)+\sin(Y)=\sin(X)+\sin(-X)=0$

$\tan(X)+\tan(Y)=\tan(X)+\tan(-X)=0$

$\cos(X)+\cos(Y)=\cos(X)+\cos(-X)=2\cos(X)$ , this is not always equal to $0$ ,

for example : if $X=0$ , then $Y=0$ ,and $\cos(X)+\cos(Y)=\cos(0)+\cos(0)=2$

What about when $X = -Y = \frac{\pi}{2}$ ? $\tan(X)$ is not defined.

Huan Bui - 2 years, 5 months ago