A Trigonometric Identity Probelm

[cse63146]

[SOLVED] A Trigonometric Identity Probelm

If I have $$sin^2 2x$$ would I be able to apply the identity $$sin^2x = (1/2)(1-cos2x)$$ to get this:

$$sin^2 2x = 2(1/2)(1 - cos^2 x)$$

Similarly, if I had $$sin^2 2x + cos^2 2x$$ would I be able to use the identity $$sin^2 x + cos^2 x = 1$$ to get:

$$sin^2 2x + cos^2 2x = 2$$

 

[MATdaveLACK]

So in your case theta = 2x
sin^2(2x)= 1/2(1-cos(4x))

 

[MATdaveLACK]

For the second half of your question, sin^2(2x) + cos^2(2x) = 1 (NOT 2)

Think about it, sin^2(x) + cos^2(x) = 1 for every value of x. So the range for x is (-infinity, +infinity). And of course 2x falls in that range (every real # falls in that range)
This applies as long as the angles are the same for both sin^2 and cos^2.

 

[cse63146]

That explains a lot. I appreciate it, thank you.