Is this correct? simplify 1/sqrt(x^2 - 9^2) when...

[Guest]

Is this correct?
Simplify
1/ sqrt(x^2 - 9^2) when x = 9 cosec theta

I use the trig identity cot^2 (x) + 1 = cosec^2 (x)

my working is as follows...

1/sqrt(81 cosec^2theta - 1)
= 1/9*sqrt(cosec^2theta -1)
= 1/9*sqrt(cot^2theta)
= 1/9cottheta
= tanx/9

 

[soroban]

Hello, americo74!

You dropped a pair of parentheses, but your result is correct.

Is this correct?
Simplify: \(\displaystyle \,\frac{1}{\sqrt{x^2\,-\,81}}\,\) when \(\displaystyle x\,=\,9\,\csc\theta\)

I used the trig identity: \(\displaystyle \,\cot^2x\,+\,1\:=\:\csc^2x\)

I assume your steps went something like this:

\(\displaystyle \frac{1}{\sqrt{81\csc^2\theta\,-\,81}}\;=\:\frac{1}{\sqrt{81(\csc^2\theta\,-\,1)}}\;= \;\frac{1}{\sqrt{81}\,\sqrt{\csc^2\theta\,-\,1}} \;=\;\frac{1}{9\sqrt{\cot^2\theta}} \;=\;\frac{1}{9\,\cot\theta}\;=\;\frac{1}{9}\,\tan x\)

 

[Guest]

Soroban, thank you for saying that my steps are correct!

Your steps seem correct too and they seem to be like mine...