# Thread: Expressing in terms of sin.

1. ## Expressing in terms of sin.

I'm having a little trouble on this problem. Any insight?

Express in terms of sin.

$\frac{1 + \cos\Theta} {\sin\Theta} + \frac{\sin\Theta} {1 + \cos\Theta}$

2. (1 + cosO)(1 + cosO) + sin0 / sin0( 1 + cosO )
1 + 2cos0 + cos0^2 + sin0^2 / sin0( 1 + cosO )
1 + 2cos0 + 1 / sin0( 1 + cosO ) take note cos0^2 + sin0^2 = 1
2 + 2cos0 / sin0( 1 + cosO )
2( 1 + cosO ) / sin0( 1 + cosO )
2/ sin0

3. Thanks, although I figured out the correct answer is actually $\frac{2} {\sin\Theta}$, but your work helped me.

4. Hello, Intrusion!

Another approach . . .

Express in terms of $\sin\theta$

. . $\frac{1 + \cos\theta}{\sin\theta} + \frac{\sin\theta} {1 + \cos\theta}$
Multiply the second fraction by $\frac{1-\cos\theta}{1-\cos\theta}$

. . $\frac{1+\cos\theta}{\sin\theta} + \frac{\sin\theta}{1 + \cos\theta}\cdot{\color{blue}\frac{1-\cos\theta}{1 - \cos\theta}} \;=\; \frac{1+\cos\theta}{\sin\theta} + \frac{\sin\theta(1 - \cos\theta)}{1-\cos^2\!\theta}$

. . $= \;\frac{1+\cos\theta}{\sin\theta} + \frac{\sin\theta(1 - \cos\theta)}{\sin^2\!\theta} \;=\;\frac{1+\cos\theta}{\sin\theta} + \frac{1 - \cos\theta}{\sin\theta}$ . $= \;\frac{2}{\sin\theta}$