Question

LIMITES Y DERIVADAS --TRIGONOMETRIA UNI

Answer 1

1. S2: $OF=\cos \theta \wedge EF=\sin\theta\to \mathbb{S}_2=\cos\theta\sin \theta$

2. S1:

$1-OC=CB\cot (\theta/2)\to 1-CB\cot (\theta/2)=OC\\1-OA=AB\cot(45-\theta/2)\to 1-CB=OC\cot(45-\theta/2)\\\\1-CB=[1-CB\cot (\theta/2)]\cot(45-\theta/2)\\\tan(45-\theta/2)-CB\tan(45-\theta/2)=1-CB\cot (\theta/2)\\\ [\cot (\theta/2)-\tan(45-\theta/2)]CB=1-\tan(45-\theta/2)\\\\CB=\dfrac{1-\tan(45-\theta/2)}{\cot (\theta/2)-\tan(45-\theta/2)}=1-\cos\theta\\\\OC=1-\sin\theta\\\\\\\mathbb{S}_1=(1-\cos\theta)(1-\sin\theta)$

$L=\lim\limits_{\theta\to0}\dfrac{(1-\cos\theta)(1-\sin\theta)}{\cos\theta\sin\theta}\\\\\\L=\lim\limits_{\theta\to0}\dfrac{\sin\theta\cos\theta}{(1+\cos\theta)(1+\sin\theta)}\\\\L=0$