State the limits for B if given that B is an obtuse angle and
a) tan2B is negative
b) tan4B is positive
c) tan2B is negative or tan 4B is positive
@Trefoil2727, Why do you keep posting a list of question, but show no effort?
From the given we know $\displaystyle \frac{\pi}{2}<B<\pi$. So any answer must be a subset of that.
a) if $\displaystyle \tan(2B)<0$ then it must be that $\displaystyle \frac{3\pi}{2}<2B<2\pi$
Now you do some work and show us.
It is clear to me that you don't understand much of this, do you?
From the given it must be true that $\displaystyle 90^o<B<180^o$. Thus any answer you find must be in that range.
If $\displaystyle \tan(2B)<0$ then $\displaystyle 270^o<2B<360^o$ or $\displaystyle 135^o<B<180^o$, which is in that range.
If $\displaystyle \tan(4B)>0$ then it could be $\displaystyle 180^o<4B<270^o$ or $\displaystyle 45^o<B<67.5^o$, which is NOT in that range.
So we must take another course.
Suppose that $\displaystyle 4B\in\text{quad } I$ or $\displaystyle 360^o<4B<450^o$ then $\displaystyle \tan(4B)>0$.
Solving we get $\displaystyle 90^o<B<112.5^o$, which is in the range.