If sinx−cosx=1/2 then cot^2 (2x)=a/ b, where a and b are coprime positive integers. What is the value of a+b ?
sinx - cosx = 1/2
square both sides
sin^2 x - 2sinxcosx + cos^2 x = 1/4
1 - sin(2x) = 1/4
sin(2x) = 3/4
after making a sketch of a right-angled triangle, the length of the other side is √7
then cot (2x) = √7/3
cot^2 (2x) = 7/9
so the a/b = 7/9 and a+b = 16
btw, I have seen quite a few questions that have this a+b stuff at the end.
Are these questions from a new textbook?
Are these on-line problems and this is how they expect the input for anwers?
Just curious.