1. if f(x) = mode of sinx + mode of cosx..what will be period of the function..?? ans is pi/2 bt how ..as periods of modesinx & modecosx is pi..2. period of f(x) = cos(cosx) +cos(sinx).??

Yes u r right period of modsinx= modcosx= pi but the period of function will be pi/2 because by definition period is the smallest possible value for which f(x) = f(x+p) this can be found out by hit and trial only (subs pi/2 in equation )

For the second function also by hit and trial period is pi/2 

dont go for definition or taking LCM when addition of cos and sin or cos cos is involved try putting pi/2, pi 2pi etc for the period

Approved

1 sol: for any equation period is f(x)=f(t+x) so when we equate the function equal to f(x) the minimum value of t we get is pi/2

so answer is pi/2...while considering mode sinx and cosx separately it is another case,.......

2.and the answer for this answer is also pi/2 as the same principle we used in the previous question

Approved