Question

Write the following in terms of sin θ only. cot θ

Answer 1

$\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)} \\\\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\\\ cos(\theta)=\pm\sqrt{1-sin^2(\theta)}\\\\ -----------------------------\\\\ cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\implies cot(\theta)=\cfrac{\pm\sqrt{1-sin^2(\theta)}}{sin(\theta)}$