Double-Angle Identity, so close yet so far.

[jddoxtator]

Trying to figure out this double angle identity.
I can get it close, but I can't figure out how to complete the LHS after the last step.

Edit: I noticed that if I break the order of operations and add before multiplying, I can force it to work, but I don't think I can do that.

 

[lev888]

Trying to figure out this double angle identity.
I can get it close, but I can't figure out how to complete the LHS after the last step.

Edit: I noticed that if I break the order of operations and add before multiplying, I can force it to work, but I don't think I can do that.

sin^2(2x) = ?

 

[jddoxtator]

sin^2(2x) = ?

2 sin^2(x) cos^2(x) , does it not?
Or is it expecting 1 - cos^2(2x)?

 

[lev888]

2 sin^2(x) cos^2(x) , does it not?
Or is it expecting 1 - cos^2(2x)?

Include intermediate steps.

 

[jddoxtator]

Not sure I am seeing intermediate steps.
The direct identities are sin(2x) = 2 sin(x) cos(x) and sin^2(x) = 1 - cos^2(x).

 

[Dr.Peterson]

2 sin^2(x) cos^2(x) , does it not?

Take it slowly, to avoid silly errors:

[imath]\sin^2(2x)=(\sin(2x))^2=(\dots)^2[/imath]

 

[lev888]

Not sure I am seeing intermediate steps.
The direct identities are sin(2x) = 2 sin(x) cos(x) and sin^2(x) = 1 - cos^2(x).

Let's say you are helping someone with a math problem. He shows you his solution. You check each line. Line 5 is correct, line 6 is wrong. What do you do?

 

[jddoxtator]

Take it slowly, to avoid silly errors:

[imath]\sin^2(2x)=(\sin(2x))^2=\dots?[/imath]

ok, so it is not a direct relation, but has to be factored.
I will try that.
I figured the rule would be constant no matter the raised power.

Edit: Ok, I got it in 5 lines now. Turns out you must pay attention to powers when using identities and cannot just substitute the power in the functions place. learn something new every day.

 

[Dr.Peterson]

ok, so it is not a direct relation, but has to be factored.
I will try that.
I figured the rule would be constant no matter the raised power.

Edit: Ok, I got it in 5 lines now. Turns out you must pay attention to powers when using identities and cannot just substitute the power in the functions place. learn something new every day.

Please show your corrected work, so others can learn what you learned (and there may be more to say about it). I wouldn't say the main idea is "factoring", but it is related.

Actually, you have to pay attention to all sorts of details, and can never blindly substitute!