Precalculus Practice, need help fast, thank you

[Sethrt]

Could you please solve and explain the process of solving this question, it's an emergency, thank you.

if (tan^3 theta-1/ tan theta-1)- sec^2 theta -1=0, find cot theta.

 

[soroban]

Hello, Sethrt!

There seems to be no solutions . . .

\(\displaystyle \text{If }\,\dfrac{\tan^3\theta-1}{\tan\theta-1}-\sec^2\theta -1\:=\:0,\,\text{ find }\cot\theta\)

We note immediately that: .\(\displaystyle \tan\theta \,\ne\, 1\)


The numerator is a difference-of-cubes; factor and reduce.

. . \(\displaystyle \dfrac{(\tan\theta-1)(\tan^2\theta + \tan\theta + 1)}{\tan\theta - 1} - \sec^2\theta - 1 \;=\;0\)


. . . . . . \(\displaystyle \tan^2\theta + \tan\theta + 1 - \sec^2\theta - 1 \;=\;0\)


. . . . . . . . . . \(\displaystyle \tan\theta \;=\;\underbrace{\sec^2\theta - \tan^2\theta}_{\text{This is 1}} \)

Therefore: . . . . . . . . \(\displaystyle \tan\theta \;=\;1\;\;(?)\)

\(\displaystyle \text{There are no solutions.}\)

 

[lookagain]

Could you please solve and explain the process of solving this question, it's an emergency, thank you.

if (tan^3 theta-1/ tan theta-1)- sec^2 theta -1=0, find cot theta.

Sethrt,

you have inappropriate requests. Please read the following:

http://www.freemathhelp.com/forum/threads/41538-Read-Before-Posting!!