Find the time period of the function f(t)=2cos(10t+1)-sin(4t-1)

how u prove this property

but Ma'am i want to know that the time period of a function which is the adding of two another function is the LCM of those function's time period

wait ,I am attaching one more page.

why take this LCM to find time period

this is the property that when you have two functions in the like addition subtraction form then the time period is equal to lcm of two two functions...

and lcm of the fraction form is in my attached page. go through it..

ma'am can u upload the property where's form u can know

if you have any doubt, do let me know!

how may I help you?

pls describe why u take the LCM to find the the time period

what is periodic of a function?, the smallest number which when you add to the variable and the function doesn't change. Now let say you have two functions with period 2 and 3 respectively. it means, in function F1 if you add 2 the the function wouldn't change. what if you add 4 instead of 2, then also the function won't change and similarly adding 6, 8,10 will also not chnage the function. now for function F2, if you add 3, 6 , 9, then the function won't change. what is common to both the list. list1 = (2,4,6,8,...) and list2 = (3,6,9,...). 6 is common. and you know 6 is LCM of 2 and 3.

that's can understood ,l want to knowing why u take the LCM to find the time period

i just give the demonstration that you have to take LCM to fulfill the definition of period of a function.

but can u explain that the time period of a function which is the adding of two another function is the LCM of those two functions's time period

I can't explain better than this. You sould read the question again, then read my explanation. if you got it, it would be best. other than that, I don't think a better explanation even exist.

is there no proof that the time period of f() is the LCM of two other functions time period