The question is to solve
I have tried writing in terms of
and in terms of
When I caved in and looked at the mark scheme it says to using , which I didn't get. Could someone please give me a clue and or suggest another way.
Substitute 1+cot^2(2x) into the equation
Then we'll obtain cot^2(2x)-cot(2x)=0
Factorise the equation
(cot (2x))(cot (2x)-1)=0
1/ tan (2x)=0
For 1/tan (2x)=0,
tan (2x)= infinity
So 2x= 90, 270
x= 45, 135
1/ tan (2x)=1
Although I hadn't worked through to the solutions because I had it in my head that I had to get a quadratic in terms of a single trigonometric function.
It didn't occur to me that I could use .
It's good to know there's another approach.
Although I also now see why
Dividing the identity by .
I haven't actually worked through the problem yet, but hopefully I'll be able to now. I'll try both ways.