Thank you very much...i got mono and now this stuff is killing me
Simplify the following expressions:
1. (cscX - 1)
secX
2. tanX - secX
tanX + secX
thank you so much for you help
$\displaystyle 1. \frac{\csc{x}-1}{\sec{x}} = \frac{\frac{1}{\sin{x}}-1}{\frac{1}{\cos{x}}}$
Multiply by $\displaystyle \frac{\sin{x}\cos{x}}{\sin{x}\cos{x}}$ to get:
$\displaystyle \frac{\cos{x}-\sin{x}\cos{x}}{\sin{x}} = \frac{\cos{x}}{\sin{x}}-\cos{x} = \cot{x} - \cos{x}$
2. Multiplying by $\displaystyle \frac{\tan{x}-\sec{x}}{\tan{x}-\sec{x}}$ does the trick. Recall that $\displaystyle \tan^2{x} + 1 = \sec^2{x} \implies \tan^2{x}-\sec^2{x}=-1$
After multiplying, you should get:
$\displaystyle \frac{(\tan{x}-\sec{x})^2}{-1} = -(\tan{x}-\sec{x})^2$