Precalc Final Help!!

[haze]

Verify the idenity: (1-tanx)(1-cotx)=2-sec x csc x

 

[pka]

Change both tangent and cotangent to functions of sine and cosine.
Do it and show us what you get.

 

[Deleted member 4993]

Verify the idenity: (1-tanx)(1-cotx)=2-sec x csc x

Since few days gone by:

\(\displaystyle [1\, - \, \tan(x)]\cdot[1 \, - \cot(x)]\)

using foil

\(\displaystyle 1\, + \, [\tan(x)]\cdot[cot(x)] \, - [\tan(x) \, + \, \cot(x)]\)

\(\displaystyle 1\, + \, 1 \, - [\frac{\sin(x)}{cos(x)} \, + \, \frac{\cos(x)}{\sin(x)}]\)

\(\displaystyle 2 \, - [\frac{\sin^2(x) \, + \, \cos^2(x)}{\cos(x) \cdot \sin(x)}]\)

\(\displaystyle 2 \, - [\frac{1}{cos(x)} \, \cdot \, \frac{1}{\sin(x)}]\)

and so on...