trig

I get:

$tan (x + (pi/6)) = tan (pi - x)$ where x = theta

therefore:

$(x + (pi/6)) = (pi - x) => x = 5(pi)/12$

and then im stuck

alevel or gcse

a level but why does that mater?

tan A = tan B does NOT imply that A = B. It does imply that $A = B + n \pi$, where n is an integer.

As I said in my previous post, this is not true.

https://www.examsolutions.net/exampapers/edexcel-c3-january-2012/

the exam solution guy says what are in the brackets equal each other and youre saying they dont.

He's wrong to say that. (as you can clearly see from his own solution). He ends up with a 2nd solution $\theta =\frac{11}{12}\pi$, but it is NOT true that $\frac{11}{12}\pi + \frac{\pi}{6} = \pi - \frac{11}{12}\pi$ (LHS = pi / 12 + pi, RHS = pi / 12).

so how would you do it? can you show me please?

tan A = tan B does NOT imply that A = B. It does imply that $A = B + n \pi$, where n is an integer.

I'll give you the first line:

$\theta + \frac{\pi}{6} = \pi - \theta + n\pi$. You need to find solutions for this where n is an integer and x falls in the desired range. Basically get a formula for theta and then try some likely values for n.

I agree with your method - I understand it. why does n have to be an integer?

Because trig functions are periodic. [This is not a sufficient answer, you need to read a textbook].

Because trig functions are periodic. [This is not a sufficient answer, you need to read a textbook].

this particular question, do you know where I can find similar types I can do for practise?

A textbook?

not all text books have those specific questions.

Solving trig equations and dealing with periodicity are in the C2 spec. I find it hard to believe that any textbook (that provides a decent number of examples) will not have suitable examples for you to work through.

Bottom line: go to a bookshop or library and browse until you find a suitable textbook.