The period of the function -sin x- -cos x- is 2 -24 -

The correct option is B π/2The smallest of π/2, 2π, 4π, π is π/2 Let f(x)= |sin x|+|cos x|. ∴ f ( x+π/2 )= | sin ( x+π/2 ) |+ | cos ( x+π/2 ) | =|cos x|+| s ...

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Byju's Answer

Standard X

Mathematics

Period of a Function

The period of...

Question

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

\frac{π}{2}

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2 π

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4 π

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π

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Solution

The correct option is A $\frac{π}{2}$
The smallest of $\frac{π}{2}, 2 π, 4 π, π$ is $\frac{π}{2}$
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 $\frac{π}{2}$

Suggest Corrections

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

The correct option is A π2The smallest of π2,2π,4π,π is π2 Let f(x)=|sin x|+|cos x|. ∴ f(x+π2)=∣∣sin(x+π2)∣∣+∣∣cos(x+π2)∣∣ =|cos x|+|−sin x| =|cos x|+|sin x| =f (x) ∴ The period of given function is π2

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