Question

If $\sin 2(\frac{2}{1}.\frac{3}{2}.\frac{4}{3}.....\frac{x-1}{x-2})=1,0^{\circ }<x<{100}^{\circ }$, then the value of $x$ is equal to

• A. ${91}^{\circ }$
• B. ${80}^{\circ }$
• C. ${49}^{\circ }$
• D. ${46}^{\circ }$

Answer 1

The correct option is D ${46}^{\circ }$

$\sin 2(\frac{2}{1}.\frac{3}{2}.\frac{4}{3}.....\frac{x-1}{x-2})=1$

$\Rightarrow \sin 2(x-1)=1$

$\Rightarrow \sin 2(x-1)=\sin {90}^o$

$\Rightarrow 2(x-1)={90}^o$

$\Rightarrow 2x-2=90$
$\Rightarrow 2x={92}^o$
$\Rightarrow x={46}^o$