8cot^2 x -8

Feb 2010
21
1
Find the x-values that are solutions of the equation:

8cot^2 x -8 = 1

so far i got from cot^2x = 1

not sure how to find the solutions...without a calculator.
 
May 2010
43
7
Firstly before you type in a formula, click the sigma button (second-top row, third from the right) and make sure the formula is between the two math brackets.

You'll want to check your algebra before proceeding...I'm not sure what you did but \(\displaystyle cot^2x = 1\) isn't the right direction. Trying factoring out the 8 to start.

Are you allowed to use a calculator or not?
 

mr fantastic

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Find the x-values that are solutions of the equation:

8cot^2 x -8 = 1

so far i got from cot^2x = 1

not sure how to find the solutions...without a calculator.
As posted, the correct simplification is \(\displaystyle \cot^2 x = \frac{9}{8} \Rightarrow \cot x = \pm \frac{3}{2 \sqrt{2}} = \pm \frac{3 \sqrt{2}}{4} \Rightarrow \tan x = \pm \frac{2 \sqrt{2}}{3}\). This can only be solved using a calculator.

Unless of course the solution \(\displaystyle x = \alpha + n \pi \) and \(\displaystyle x = - \alpha + n \pi\) where \(\displaystyle \alpha = \tan^{-1} \left(\frac{2 \sqrt{2}}{3}\right)\) and \(\displaystyle n \in Z\) is acceptable ....
 
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