Question

What is cot(theta)+tan(theta)=?

csc2(theta)
2csc2(theta)
sec2(theta)
2sec2(theta)

Answer 1

\(\cot \theta + \tan \theta\)

\(= \dfrac{\cos \theta}{\sin \theta} + \dfrac{\sin \theta}{\cos \theta} \)

\(= \dfrac{\cos \theta}{\sin \theta} \times \dfrac{\cos \theta}{\cos \theta}+ \dfrac{\sin \theta}{\cos \theta} \times \dfrac{\sin \theta}{\sin \theta}\)

\(= \dfrac{\cos^2 \theta}{\sin \theta \cos \theta} + \dfrac{\sin^2 \theta}{\sin \theta \cos \theta} \)

\(= \dfrac{\cos^2 \theta + \sin^2 \theta}{\sin \theta \cos \theta}\)

\(= \dfrac{1}{\sin \theta \cos \theta}\)

\(= \sec \theta \csc \theta\)

\(= 2 \csc 2 \theta\)