C3, Exam question (trig)

Please help me solve 9iii,

Please help me solve 9iii,

not able to see it...

could you post it in imagepost.org and link from there ?

Just use https://imgur.com/ or something to upload images then link them here. By now it should be obvious that TSR's image upload procedure is terrible.

Please help me solve 9iii,

For 9iii you need to use the identity in part (i) and obtain a quadratic in $\tan \theta$ while $k^2$ would just be some constant. From there, you want to show that $b^2 - 4ac > 0$. This is C1 stuff, except you got tan as the variable.

For 9iii you need to use the identity in part (i) and obtain a quadratic in $\tan \theta$ while $k^2$ would just be some constant. From there, you want to show that $b^2 - 4ac > 0$. This is C1 stuff, except you got tan as the variable.

That doesnt work, here is what the Answer says, However I dont understand the bit in red. (I got the equation)

It does work it's just a different approach and requires a bit of alternative thinking, though I did misread the question initially so this isn't the best approach.

As for the red bit, the RHS is always positive - this should be obvious - and so the root of that will yield that $\tan \theta$ can be strictly +ve or strictly -ve. In either case, there will be a single solution for each (consider the graph of $\tan \theta$ for $0 < \theta < \pi$, which coveres the +ve and -ve values exactly once.)

What is a quadrant

It's probably referring to CAST diagram. I don't use them so I can't say.

What is a quadrant