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Question Number 7200 by Tawakalitu. last updated on 16/Aug/16

$$Provethat$$$$\frac{sin\left(\frac{\mathrm{\Theta }}{2}\right)}{\left(\frac{\mathrm{\Theta }}{2}\right)}=1$$

Commented by Rasheed Soomro last updated on 16/Aug/16

$$Doyoumean\underset{\mathrm{\Theta }\to 0}{\lim }\frac{\sin \left(\frac{\mathrm{\Theta }}{2}\right)}{\frac{\mathrm{\Theta }}{2}}=1?$$

Commented by Tawakalitu. last updated on 16/Aug/16

$$yessir$$

Commented by FilupSmith last updated on 17/Aug/16

$$L=\underset{x\to 0}{\lim }\frac{\sin x}{x}$$$$L^{\prime }{Hopital}^{\prime }sLaw$$$$L=\underset{x\to 0}{\lim }\frac{\cos x}{1}$$$$L=\underset{x\to 0}{\lim }\cos \left(0\right)$$$$L=1$$

Commented by Tawakalitu. last updated on 17/Aug/16

$$Thankyouforyourhelp.$$

Answered by Rasheed Soomro last updated on 16/Aug/16

$$\underset{\mathrm{\Theta }\to 0}{\lim }\frac{\sin \left(\frac{\mathrm{\Theta }}{2}\right)}{\frac{\mathrm{\Theta }}{2}}=1$$$$----------------$$$$Let\frac{\mathrm{\Theta }}{2}=\alpha ,thenas\mathrm{\Theta }\to 0\Rightarrow \alpha \to 0$$$$\underset{\mathrm{\Theta }\to 0}{\lim }\frac{\sin \left(\frac{\mathrm{\Theta }}{2}\right)}{\frac{\mathrm{\Theta }}{2}}=1\Rightarrow \underset{\alpha \to 0}{\lim }\frac{\sin \alpha }{\alpha }=1$$$$Whichisawellknowntheormofcalculus.$$$$Henceproved.$$

Commented by Tawakalitu. last updated on 16/Aug/16

$$Thankyouverymuch.iappreciate.$$

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