Question

I am lost on what to do

Answer 1

`\bf sin({{ \alpha}})sin({{ \beta}})=\cfrac{1}{2}[cos({{ \alpha}}-{{ \beta}})\quad -\quad cos({{ \alpha}}+{{ \beta}})] \\\\\\ cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\\\\ -----------------------------\\\\ \lim\limits_(x\to 0)\ \cfrac{sin(11x)}{cot(5x)}\\\\ -----------------------------\\\\ \cfrac{sin(11x)}{(cos(5x))/(sin(5x))}\implies \cfrac{sin(11x)}{1}\cdot \cfrac{sin(5x)}{cos(5x)}\implies \cfrac{sin(11x)sin(5x)}{cos(5x)}`


`\bf \cfrac{(cos(11x-5x)-cos(11x+5x))/(2)}{cos(5x)}\implies \cfrac{(cos(6x)-cos(16x))/(2)}{cos(5x)} \\\\\\ \cfrac{cos(6x)-cos(16x)}{2}\cdot \cfrac{1}{cos(5x)}\implies \cfrac{cos(6x)-cos(16x)}{2cos(5x)} \\\\\\ \lim\limits_(x\to 0)\ \cfrac{cos(6x)-cos(16x)}{2cos(5x)}\implies \cfrac{1-1}{2\cdot 1}\implies \cfrac{0}{2}\implies 0`