Plz expain how to solve dis V n∈N 1) sin(nx) sinx2) sin(nx) nsinx3) - Maths - Principle of Mathematical Induction

Question

Plz expain how to solve dis

V   n ∈ N

1 )   sin ( n x ) < sin x 2 )     sin ( n x )
< n sin x 3 )     sin ( n x ) ≤ n sin x 4 )  
sin ( n x ) ≤ sin n

Brijendra Pal · Accepted Answer

Hi,
Taking third option,

For n=0, |sin(n*0)| = 0, n|sin(x)| = 0 is true

Suppose that |sin(nx)| ≤ n|sin(x)|
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_59f34aa11a01a%20png"
style="width: 589px; height: 99px;">

So it is true

Plz expain how to solve dis... V n ∈ N 1 ) sin ( n x ) < sin x 2 ) sin ( n x ) < n sin x 3 ) sin ( n x ) ≤ n sin x 4 ) sin ( n x ) ≤ sin n

Plz expain how to solve dis...

$V n \in N$

$1) |\sin (n x)| < |\sin x| 2) |\sin (n x)| < n |\sin x| 3) |\sin (n x)| \leq n |\sin x| 4) |\sin (n x)| \leq \sin n$