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