Question

Simplify the trigonometric expression: tanθ + ctanθ

Answer 1

`\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\qquad sin^2(\theta)+cos^2(\theta)=1\\\\ -------------------------------\\\\ tan(\theta )+cot(\theta )\implies \cfrac{sin(\theta)}{cos(\theta)}+\cfrac{cos(\theta)}{sin(\theta)}\implies \cfrac{sin^2(\theta)+cos^2(\theta)}{cos(\theta)sin(\theta)} \\\\\\ \cfrac{1}{cos(\theta)sin(\theta)}\implies \cfrac{1}{cos(\theta)}\cdot \cfrac{1}{sin(\theta)}\implies sec(\theta)csc(\theta)`