Question

if x= secθ +tanθ than x+1/x=?

Answer 1

$$\text{if } x = \sec\theta + \tan\theta \text{ than } x + \frac{1}{x} = ?$$ $$\sec\theta = \frac{1}{\cos\theta}, \tan\theta = \frac{\sin\theta}{\cos\theta}$$ $$\text{So } x = \frac{1 + \sin\theta}{\cos\theta}$$ $$\text{then } x + \frac{1}{x} = \frac{\cos\theta}{1 + \sin\theta} + \frac{1 + \sin\theta}{\cos\theta} = \frac{(1 + \sin\theta)^2 + \cos^2\theta}{\cos\theta(1 + \sin\theta)} = \frac{1 + 2 * \sin\theta + \sin\theta^2 + \cos^2\theta}{\cos\theta(1 + \sin\theta)} =$$ $$\frac{2 + 2 * \sin\theta}{\cos\theta(1 + \sin\theta)} = \frac{2(1 + \sin\theta)}{\cos\theta(1 + \sin\theta)} = \frac{2}{\cos\theta} = 2\sec\theta.$$