Question

period of function f(x)= Sin(x/4) + cos(4x/5)​

Answer 1

HEYA! HERE YOU GO!

What is the period of the function y=sin^4x + cos^4x?

The period of this function is (pi/2)

When we add two functions

f(x)=g(x)+h(x)

If g(x) and h(x) are periodic with fundamental periods T1 and T2. Then the fundamental period of f(x) will be

T3=l.c.m(T1,T2)

Also if you square a function then the time period will reduce to half of the initial if the function has range including both negative and positive outputs. If only positive or only negative outputs are the range of any function then the time period does not change.

Hence here,

When sin(x) is squared the time period changes by half. But when sin^2(x) is squared then the time period remains same. Similarly for cos(x) also

Thus for both cos^4(x) and sin^4(x) the fundamental period is (pi). And the lcm of pi and pi is also pi.

Hence the time period is (pi)/2.

HOPE THIS HELPS YOU BUDDY!