How tonsolve this?

__________________________-____________________

let theta=t and cost=y

then y=plus minus 1/2root2

when y is positive, t can have 2 values in 0 to 2pi, one is in 0 to pi/2 (call it t1) and other is in 3pi/2 to 2pi (call it t4)

when y is negative, t can have 2 values in 0 to 2pi, one is in pi/2 to pi (call it t2) and other is in pi to 3pi/2 (call it t3).

so the values satisfying in 0 to 4pi in ascending order are:

t1, t2, t3, t4, t1+2pi, t2+2pi, t3+2pi, t4+2pi

so 2 APs can be formed as follows:

t1, t3, t1+2pi, t3+2pi

and t2, t4, t2+2pi, t4+2pi

so the common difference has to be pi.

 

But the answer given here is

Four AP are formed................................................

Whom should I consider true?

Book or you? 

Well, sometimes askiitians can get as frustrating as can get. The website design has so many bugs! I just wrote a long answer but due to technical error it didn't show up. :( Only had they put some more effort.

There is a channel on YouTube called DOUBTNUT and it has the exact same problem that you have asked above. And his answer and explanation matches with what I have written. So my advice to you would be to go get some good and standard books rather than picking up books off the streets and then getting caught in confusion.

Ohh ,please think before wrirtng anything sir,

This problem is from India's most trusted institute

Allen material, I don't think so it is wrong.

I haven't picked it from street.

Very bad experience today.......😢😢

Ok I will consider you right................. ..................

|______________________________________________

Ok so first thing sorry if I sounded rude to you. 

Next thing I have myself studied from Allen institute and I was in the top batch. Aman Bansal and me were in the same batch xd. 

Now lemme comment on Allen's material. Idk if it has changed now, but in my time Allen modules sucked for the most part, and the wuesquest were easy enough to be skipped. The only thing practice worthy was exercise 4B. 

If you are looking to practice some real good material, I would suggest fiitjee and resonance modules. I only had just one practice module of math from resonance and it was perfection. Also, fiitjee modules are top class.

Btw, all the best for your preparations!