limiting sum. (1 Viewer)

[crammy90]

2004 HSC Q9 a ii
so r is -tan^2(theta)
for what values of theta in the interval -pi/2 < theta < pi/2 does the limiting sum of the series exist.
i get the working up upto here
-1< tan^2(theta) < 1
then i dont get this...
"since tan^2(theta) > 0, only need to solve tan^(theta) <1
:SSSSSS
and then
"when tan(theta) = +- 1, theta = +-(pi/4)
since y = tan theta is an increasing fuction, this means the solution is:
-pi/4 < theta < pi/4

what are they doing ? why is it only need to solve 1 side of the eqality thing and where do they get the +-1
thanks

 

[addikaye03]

absv.-tan^2@<1, by definitio of absoute value, u can eliminate the negative and the next part they have used difference of sqaures, (tan@-1)(tan@+1)<0... i think thats right.