The period of f(x)= mod of sinx+mod og cosx?

Question

Answer

T” is said to be the period of a function f(x) if and onlyif f(x) = f(x + T).

Consider f(x) = |sin x| + |cos x|. Now,

f(x + π/2) = |sin(x + π/2)| + |cos(x + π/2)|

=|cos x| + |-sin x|

=|sin x| + |cos x|

=f(x)

Therefore the period of f(x) is π/2

Answer

Period of f(x)= |sinx|+|cosx|

To determine the period of f(x)= |sinx|+|cosx|, we need to first understand the period of the individual functions sinx and cosx.

Period of sinx

The function sinx is a periodic function with a period of 2π. This means that sin(x+2π) = sinx for all values of x.

Period of cosx

The function cosx is also a periodic function with a period of 2π. This means that cos(x+2π) = cosx for all values of x.

Period of |sinx|+|cosx|

Now, let's consider the function f(x)= |sinx|+|cosx|. We can rewrite this function as:

f(x)= |sinx|+|cosx| = |sin(x+π/2)| + |cos(x)|

Since sin(x+π/2) = cosx, we can simplify the function as:

f(x)= |sinx|+|cosx| = |cosx| + |cosx| = 2|cosx|

Conclusion

The period of f(x)= |sinx|+|cosx| is π.