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

Printable View

- Dec 2nd 2008, 01:24 AMkrizzle13Simplify Trig Identities
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 - Dec 2nd 2008, 01:34 AMChop Suey
$\displaystyle 1. \frac{\csc{x}-1}{\sec{x}} = \frac{\frac{1}{\sin{x}}-1}{\frac{1}{\cos{x}}}$

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:

$\displaystyle \frac{(\tan{x}-\sec{x})^2}{-1} = -(\tan{x}-\sec{x})^2$ - Dec 2nd 2008, 02:13 AMkrizzle13
thank you so much...makes sense now