Relearning a little bit of trig

[dolomite]

I'm trying to relearn some trig for a math placement test to put me into a calculus class and am having trouble with one particular problem. One of the example problems is as follows:

Find cos^2(2x)+sin^2(2x)

I know the trig identity cos^2(x)+sin^2(x)=1 but I don't know how to apply this, if it should be applied at all, to the problem given. Could I get some help?

 

[Vid]

Let u = 2x. Then...

 

[thomas49th]

then where?

 

[icystrike]

I'm trying to relearn some trig for a math placement test to put me into a calculus class and am having trouble with one particular problem. One of the example problems is as follows:

Find cos^2(2x)+sin^2(2x)

I know the trig identity cos^2(x)+sin^2(x)=1 but I don't know how to apply this, if it should be applied at all, to the problem given. Could I get some help?

you need to see what do they wan to acquire when you simplify it.. you got to see the factors in the RHS or while you are solving.

 

[redargon]

yeah, well cos^2(u)+sin^2(u)=1
therefore cos^2(2x)+sin^2(2x)=1

ie as long as the two angles are the same, the sum of the sin squared and cos squared of that angle is always 1.

 

[icystrike]

yeah, well cos^2(u)+sin^2(u)=1
therefore cos^2(2x)+sin^2(2x)=1

ie as long as the two angles are the same, the sum of the sin squared and cos squared of that angle is always 1.

he meant when to apply tat substitution whr by we sub in cos²(2x)+sin²(2x) = 1
or when to leave it alone.

 

[redargon]

ok, I thought it was a simpler question than that, thought he didn't quite grasp the identity concept, that's all. We very seldom sub in cos²(2x)+sin²(2x) = 1 but rather cos²(x)+sin²(x) = 1.

 

[icystrike]

ok, I thought it was a simpler question than that, thought he didn't quite grasp the identity concept, that's all. We very seldom sub in cos²(2x)+sin²(2x) = 1 but rather cos²(x)+sin²(x) = 1.

exactly! for the thread starter: practice is the key !