The period of the function | s i n x | + | c o s x | is Options: A . &nbsp π 2 B . &nbsp 2 π C . &nbsp 4 π D . &nbsp π

The period of the function |sinx|+|cosx| is

Question -

The period of the function $| s i n x | + | c o s x |$ is

Options:

A .

\frac{π}{2}

B .

2 π

C .

4 π

D .

π

Answer: Option A
:
A
The smallest of

\frac{π}{2}, 2 π, 4 π, π

\frac{π}{2}

Let

f (x) = | s i n x | + | c o s x | .

∴ f (x + \frac{π}{2}) = ∣ ∣ s i n (x + \frac{π}{2}) ∣ ∣ + ∣ ∣ c o s (x + \frac{π}{2}) ∣ ∣

= | c o s x | + | - s i n x |

= | c o s x | + | s i n x |

=f (x)

∴

The period of given function is

\frac{π}{2}

Was this answer helpful ?

Next Question