1. ## 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?

2. ## Re: trig identity question

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 $\tan^2(x)=\sec^2(x)-1$.

3. ## Re: trig identity question

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..

4. ## Re: trig identity question

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

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

5. ## Re: trig identity question

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.