Question

The general solution of cot θ + tan θ = 2 is ______.

Options

• θ = ${\displaystyle \frac{\text{n}\pi }{2}+{(-1)}^{\text{n}}\frac{\pi }{4}}$

• θ = ${\displaystyle \text{n}\pi +{(-1)}^{\text{n}}\frac{\pi }{8}}$

• θ = ${\displaystyle \frac{\text{n}\pi }{2}+{(-1)}^{\text{n}}\frac{\pi }{8}}$

• θ = ${\displaystyle \frac{\text{n}\pi }{2}+{(-1)}^{\text{n}}\frac{\pi }{6}}$

Answer 1

The general solution of cot θ + tan θ = 2 is θ = ${\displaystyle \frac{\text{n}\pi }{2}+{(-1)}^{\text{n}}\frac{\pi }{4}}$.

Explanation:

cot θ + tan θ = 2

∴ ${\displaystyle \frac{1}{\tan \theta }+\tan \theta }$ = 2

⇒ 1 + tan²θ = 2 tan θ

∴ ${\displaystyle \frac{2\tan \theta }{1+{\tan }^2\theta }}$ = 1

⇒ sin 2θ = 1

⇒ 2θ = ${\displaystyle \text{n}\pi +{(-1)}^{\text{n}}\frac{\pi }{2}}$

⇒ θ = ${\displaystyle \frac{\text{n}\pi }{2}+{(-1)}^{\text{n}}\frac{\pi }{4}}$