# trig identity question

• Mar 8th 2014, 09:44 AM
ameerulislam
trig identity question
if
sec^2 x - tan^2 x =1

is sec^4 x - tan^4 x =1 or any other bigger even power will also be like this?
• Mar 8th 2014, 10:02 AM
Plato
Re: trig identity question
Quote:

Originally Posted by ameerulislam
if
sec^2 x - tan^2 x =1

is sec^4 x - tan^4 x =1 or any other bigger even power will also be like this?

NO!

That is true because $\tan^2(x)=\sec^2(x)-1$.
• Mar 8th 2014, 10:20 AM
ameerulislam
Re: trig identity question
Quote:

Originally Posted by Plato
NO!

That is true because $\tan^2(x)=\sec^2(x)-1$.

ok, so is there any work around like $(\tan^2(x))^2=(\sec^2(x))^2-1$
sorry if I sound stupid..
• Mar 8th 2014, 10:31 AM
ameerulislam
Re: trig identity question
my original problem was $\int \frac{(3x^3)}{\sqrt {x^2-25}} dx$

used trig substitution technique to substitute $x, x=a sec^2x$
• Mar 8th 2014, 11:00 AM
Plato
Re: trig identity question
Quote:

Originally Posted by ameerulislam
my original problem was $\int \frac{(3x^3)}{\sqrt {x^2-25}} dx$

used trig substitution technique to substitute $x, x=a sec^2x$

Use $x=5 sec(u)$ then $dx=5\tan(u)\sec(u)du$

Notice that $\sqrt{25\sec^2(u)-25}=5\sqrt{\sec^2(u)-1}$

This should a lesson: Post the actual question first.