Ask Me Help Desk - Simplify cosxcscxtanx

Quote:

Originally Posted by BigTreeWoody

Simplify cos(x)csc(x)tan(x)
Verify that tan(x)csc(x)=sec(x)

The definition of csc(x) = 1/sin(x)
The definition of sec(x) = 1/cos(x)
Another great thing to memorize is that tan(x) = sin(x)/cos(x)

$cos(x)\,csc(x)\,tan(x) = \frac {cos(x)}{1}\, \frac {1}{sin(x)}\, \frac {sin(x)}{cos(x)}$

the sin(x) terms will cancel; the cos(x) terms will also cancel so

$cos(x)\,csc(x)\,tan(x) = 1$

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$tan(x)csc(x)=\frac {sin(x)}{cos(x)}\, \frac {1}{sin(x)}\,=\,\frac {1}{cos(x)} \,\eq\, sec(x)$