Question

If $0<\propto <\frac{\pi }{2}$ and $x=\cos \propto -{\cos }^2\propto +{\cos }^3\propto -.....$ to $\infty$,
then,

• A. $0<x<1$
• B. $0\le x\le 1$
• C. $-1\le x\le 1$
• D. $1\le x\le 2$

Answer 1

Answer: (A)

$0<x<1$

$x=\frac{\cos \propto }{1+\cos \propto }(S_{\infty }=\frac{a}{1-r})$
$\cos \propto >0$ $\therefore$ $1+\cos \propto >\cos \propto$
$\Rightarrow$ $1>\frac{\cos \propto }{1+\cos \propto }$ $\Rightarrow$ $\frac{\cos \propto }{1+\cos \propto }<1$
$\therefore$ $0<x<1$
$\therefore$ (1) is correct