Question

What is the lim (1-cos theta)/(2sin^2 theta) as theta approahes 0?

Answer 1

`\displaystyle \lim_(\theta\to 0)(1-\cos \theta)/(2\sin ^2\theta)=\\\\ \lim_(\theta\to 0)((1-\cos \theta)(1+\cos \theta))/(2\sin ^2\theta(1+\cos \theta))=\\\\ \lim_(\theta\to 0)(1-\cos^2 \theta)/(2\sin ^2\theta+2\sin^2 \theta\cos \theta)=\\\\ \lim_(\theta\to 0)(\sin^2 \theta)/(2\sin ^2\theta+2\sin^2 \theta\cos \theta)=\\\\ \lim_(\theta\to 0)(1)/(2+2\cos \theta)=\\\\ (1)/(2+2\cdot1)=\\\\ (1)/(4)`