## A community for students. Sign up today

Here's the question you clicked on:

## anonymous one year ago cosx/ (1+sinx) + (1+sinx)/ cosx= 2secx

• This Question is Open
1. johnweldon1993

$\large \frac{cos(x)}{1 + sin(x)} + \frac{1 + sin(x)}{cos(x)} = 2sec(x)$ We need a common denominator first...what would that be?

2. johnweldon1993

We can see the first fraction is missing a factor of cos(x) on the bottom...and we can see that the second fraction is missing a factor of 1 + sin(x) so we can work with that... $\large \frac{cos(x)}{cos(x)} \times \frac{cos(x)}{1 + sin(x)} + \frac{1 + sin(x)}{1 + sin(x)} \times \frac{1 + sin(x)}{cos(x)} = 2sec(x)$ And simplify that down a bit $\large \frac{cos^2(x)}{(1 + sin(x))cos(x)} + \frac{(1 + sin(x))^2}{(1 + sin(x))cos(x)} = 2sec(x)$ Now lets put them over the common denominator $\large \frac{cos^2(x) + (1 + sin(x))^2}{(1 + sin(x))cos(x)} = 2sec(x)$ Now...what can we replace $$\large cos^2(x)$$ with?

#### Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy