SOLUTION: cos^2 5x-sin^2 5x=cos10x
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Question 326427: cos^2 5x-sin^2 5x=cos10x
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
A few things I want you to consider before I work on this problem.
You just put an equation out there without any explanation of what you wanted to do with it, what is giving you difficulty, or anything else. This sort of behavior is:
Rude
Disrespectful
Has a high probability of getting a less than helpful response
this is Algebra.com, not the Psychic Hotline.
My recommendation to you is to go back and very carefully re-read (or read in the first place) the instructions for posting questions on this site. Then, after you are certain you understand the instructions, and this is the second part of a two-part recommendation, follow the instructions.
Now, as to your equation. In fact, this is an identity, so I presume you want to demonstrate that it is an identity.
Let 
.
Then
\ =\ \cos2(\varphi)\ =\ \cos^2(\varphi)\ -\ sin^2(\varphi))
by the Cosine Double Angle Formula.
But
\ -\ sin^2(\varphi)\ =\ \cos^2(5x)\ -\ sin^2(5x))
by substitution.
Hence
\ \equiv\ \cos^2(5x)\ -\ sin^2(5x)\ \forall\ x\ \in\ \mathbb{R})
John
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