We have to solve tan(x+pi/3)=tan(pi/2-x) for values of x that satisfy 0<x<pi.

In the specified range, each value of x has a unique value of tan x.

This allows us to equate x + pi/3 and pi/2 - x to arrive at x.

x + pi/3 = pi/2 - x

...

## Unlock

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

We have to solve tan(x+pi/3)=tan(pi/2-x) for values of x that satisfy 0<x<pi.

In the specified range, each value of x has a unique value of tan x.

This allows us to equate x + pi/3 and pi/2 - x to arrive at x.

x + pi/3 = pi/2 - x

=> 2x = pi/2 - pi/3

=> 2x = (3pi - 2pi)/6

=> x = pi/12

**The required value of x = pi/12**