Question

$\lim _ { x \rightarrow 0 }$ $\frac{\cos^{2}(1 - \cos^{2}(1 - \cos^{2}(......... - \cos^{2}(x))).......)}{\sin\left\{ \pi\left( \frac{\sqrt{x + 4} - 2}{x} \right) \right\}}$ is equal to –

• A. $\frac{\pi}{4}$
• B. $\frac{4}{\pi}$
• C. $\frac{\pi}{2}$
• D. $\frac{2}{\pi}$

Answer 1

Answer: (B)

$\frac{4}{\pi}$

Answer 2

Let P

= $\lim _ { x \rightarrow 0 }$

=$\lim _ { x \rightarrow 0 }$

= $\lim _ { x \rightarrow 0 }$

=$\lim _ { x \rightarrow 0 }$

= $\frac { \cos ^ { 2 } 0 } { 1 } \cdot \frac { ( 2 + 2 ) } { \pi }$ = $\frac { 4 } { \pi }$.