please help .........

Hi student

Let sinx= t
2t² +3t – 2 = 2t² +4t -t -2 = 2t(t+2) -1(t+2)= (2t -1)(t+2)
Now given (2t-1)(t+2)>0
=> t>1/2 or t<-2
=> sinx> ½ or sinx <-2 (not possible)
So we take first one only
x – ( pi/6, 5pi/6) ….….…..(1)
For second equation x² – x-2 <0
= (x-2)(x+1)<0
=> -1<x<2 ................. (2)
Combining 1 and 2
x- (pi/6, 2)
In you have any doubts please reply on this thread.

Approved