The period of the function f(x)= cos 4x+ tan 3x is

Question

The period of the function f(x)= cos 4x+ tan 3x is (A) (π/12) (B) (π/6) (C) (π/2) (D) π

Tardigrade Admin · Accepted Answer

We have, f(x)= cos 4 x+ tan 3 x Clearly, period of cos 4 x is (2 π/4)=(π/2) and that of tan 3 x is (π/3) ∴ Period of f(x)=( operatornameLCM text of (π text and π)/H C F text of (2 text and 3)) =(π/1)=π

Q. The period of the function $f (x) = cos 4 x +$ tan $3 x$ is

$\frac{π}{12}$

$\frac{π}{6}$

$\frac{π}{2}$

$π$

$2 π$

We have, $f (x) = cos 4 x + tan 3 x$
Clearly, period of $cos 4 x$ is $\frac{2 π}{4} = \frac{π}{2}$ and that of $tan 3 x$ is $\frac{π}{3}$
$∴$ Period of $f (x) = \frac{LCM of ( π and π )}{H CF of ( 2 and 3 )}$
$= \frac{π}{1} = π$

Q. The period of the function f(x)=cos4x+ tan 3x is

12π​

6π​

2π​

π

2π

We have, f(x)=cos4x+tan3x Clearly, period of cos4x is 42π​=2π​ and that of tan3x is 3π​ ∴ Period of f(x)=HCF of (2 and 3)LCM of (π and π)​ =1π​=π