Let us consider the trigonometric equation:-

sinx = mod cosx

It is being asked to calculate the number of solutions of this equation in the interval (0,4pi).

Now there are two ways to solve this equation.

1)Firstly, considering two graphs y = sinx & y = mod cosx, the number of points in (0,4pi) where these graphs intersect is 4. Hence the number of solutions is 4.

2)We may write the equation as sinx = +-cosx. Dividing LHS and RHS by cosx (Here, cosx can't be 0 as when cosx =0, sinx =1 or -1 which isn't possible as sinx = mod cosx) , we have, tanx = +-1

Now, tanx =+-1 gives 8 solutions in (0,4pi) which contradicts the first method.

Can u point out the flaw in the second method?!!!!!!

dude, the equation sinx = |cosx|

does not mean sinx = +- cosx

it means sinx = cosx, cosx >=0

sinx = - cosx, cosx < 0

and you cannot combine the two.

now this gives you 4.

 Correct

Look carefully at the question sarang........The interval is (0,4pi) and not (0,2pi)