Question

If $x,x-y$ and $x+y$ are the angles of a triangle (not an equilateral triangle) such that $\tan (x-y),\tan x$ and $\tan (x+y)$ are in GP, then what is $x$ equal to?

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{2}$

Answer 1

Answer: (B)

$\frac{\pi }{3}$

we know that, Sum of Angles of a Triangle is ${180}^o$

$x+(x-y)+(x+y)={180}^o\Rightarrow 3x={180}^o=x={60}^o=\frac{\pi }{3}$

Therefore,Correct Answer is $B$