1. ## Proving identities..

Hi ya'll.

Another question that has me completely and utterly stumped.

show that:

((1+cot theta)/csc theta)) - (sec theta/(tan theta + cot theta))= cos theta

sorry about not being able to write it properly.
If you could explain what you did as well so i can follow on, that would be amazing.

Thanks

2. ## Re: Proving identities..

Hi ya'll.

Another question that has me completely and utterly stumped.

show that:

((1+cot theta)/csc theta)) - (sec theta/(tan theta + cot theta))= cos theta

sorry about not being able to write it properly.
If you could explain what you did as well so i can follow on, that would be amazing.

Thanks
$(\sin \theta)(1+\cot \theta)-\frac{1}{(\cos \theta) (\tan \theta + \cot \theta)}=\cos \theta$

$\sin \theta + \cos \theta - \frac {1}{\sin \theta + \frac{\cos^2 \theta}{\sin \theta}}=\cos \theta$

$\sin \theta + \cos \theta-\frac{\sin \theta}{1}=\cos \theta$

$\cos \theta = \cos \theta$

3. ## Re: Proving identities..

$\text{Show that: }\:\dfrac{1+\cot\theta}{\csc\theta} - \dfrac{\sec\theta}{\tan\theta + \cot\theta} \:=\:\cos \theta$

$\text{We have: }\:\dfrac{1 + \frac{\cos\theta}{\sin\theta}}{\frac{1}{\sin\theta }} - \dfrac{\frac{1}{\cos\theta}}{\frac{\sin\theta}{ \cos\theta} + \frac{\cos\theta}{\sin\theta}}$

Multiply the first fraction by $\tfrac{\sin\theta}{\sin\theta}$, the second fraction by $\tfrac{\sin\theta\cos\theta}{\sin\theta\cos\theta}$

. . $\displaystyle \frac{\sin\theta\left(1 + \frac{\cos\theta}{\sin\theta}\right)}{\sin\theta \left(\frac{1}{\sin\theta}\right)} - \frac{\sin\theta\cos\theta\left(\frac{1}{\cos\thet a}\right)}{\sin\theta\cos\theta\left(\frac{ \sin\theta}{\cos\theta} + \frac{\cos\theta}{\sin\theta}\right)}$

. . $\displaystyle=\;\frac{\sin\theta + \cos\theta}{1} - \frac{\sin\theta}{\underbrace{\sin^2\theta + \cos^2\theta}_{\text{This is 1}}}$

. . $=\;\sin\theta + \cos\theta - \sin\theta$

. . $=\;\cos\theta$

4. ## Re: Proving identities..

Thank you do much! I think i was losing it when there was just too many sin and cos. got me slightly confused.
Thanks!