Question

If $\frac{\cos x}{\sin ax}$ is a periodic function, then

$\operatorname { Lim } _ { m \rightarrow \infty }$ $\underset{n \rightarrow \infty}{Lim}$ (1 + cos^2m n!πa) is equal to –

• A. 0
• B. 1
• C. 2
• D. – 1

Answer 1

Answer: (C)

2

Answer 2

If $\frac { \cos x } { \sin a x }$ is periodic then a must be rational

A is rational n → ∞ 

n!πa will become and integral multiple of π  $\operatorname { Lim } _ { n \rightarrow \infty }$

(1 + cos^2m n!πa)

1 + (± 1)^2m ⇒ 2