# Thread: Weird Trig Identity

1. ## Weird Trig Identity

Establish each trig identity.

(1) In|tan(x)| = In|sin(x)| - In|cos(x)|

(2) In|sec(x) + tan(x)| + In|sec(x) - tan(x)| = 0

Also: Is In the symbol for natural log?

2. it's ln ... with a lower case L, no upper case I.

I think you've seen these properties of logs on this forum before, correct?

for (1) ... remember ln(a) - ln(b) = ln(a/b) ?

for (2) ... remember ln(a) + ln(b) = ln(ab) ?

3. Yes but it's not "In" it's "ln", the first character is a lowercase L not an uppercase i.

4. Originally Posted by magentarita
Establish each trig identity.

(1) In|tan(x)| = In|sin(x)| - In|cos(x)|

(2) In|sec(x) + tan(x)| + In|sec(x) - tan(x)| = 0

Also: Is In the symbol for natural log?
Why didn't you apply what you learned from logarithms in this forum here?

1.$\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}$

$\displaystyle \ln{\tan{x}} = \ln{\frac{\sin{x}}{\cos{x}}} = \ln{\sin{x}} - \ln{\cos{x}}$

2. $\displaystyle \ln{(\sec{x} + \tan{x})} + \ln{(\sec{x} - \tan{x})}$

$\displaystyle \ln{[(\sec{x} + \tan{x})(\sec{x} - \tan{x})]}$

$\displaystyle \ln{(\sec^2{x} - \tan^2{x})}$

You should know that $\displaystyle 1 + \tan^2{x} = \sec^2{x}$

Thus:
$\displaystyle \ln{1} = 0$

5. ## Thanks...

I thank you all, especially Chop Suey.