# Thread: Rewrite in terms of tan x

1. ## Rewrite in terms of tan x

I failed this exam miserably.. Please help me correct this!

Rewrite (sec x + csc x) ( sin x + cos x) -2-cot x in terms of tan x

I appreciate your help!

2. ## Re: Rewrite in terms of tan x

Originally Posted by Calcgirl
I failed this exam miserably.. Please help me correct this!

Rewrite (sec x + csc x) ( sin x + cos x) -2-cot x in terms of tan x

I appreciate your help!
\displaystyle \begin{align*} \left(\sec{x} + \csc{x}\right)\left(\sin{x} + \cos{x}\right) - 2 - \cot{x} &= \left(\frac{1}{\cos{x}} + \frac{1}{\sin{x}}\right)\left(\sin{x} + \cos{x}\right) - 2 - \cot{x} \\ &= \frac{\sin{x}}{\cos{x}} + 1 + 1 + \frac{\cos{x}}{\sin{x}} - 2 - \cot{x} \\ &= \tan{x} + \cot{x} - \cot{x} \\ &= \tan{x} \end{align*}

3. ## Re: Rewrite in terms of tan x

Thank you sooo much! It makes so much sense now!

4. ## Re: Rewrite in terms of tan x

Hy,
Whenever you see the terms like sec x, cosec x, cot x try to convert these angles in the terms of cos x, sin x, tam x. This may help you a lot in solving question & also make it simpler & easier to solve the question.