Prove the following identities
These are the ones I couldn't solve from a worksheet I got in class. Please help
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Here are the last two . . . The left side is a square . . . . .
Therefore: . This one gets messy . . .
We know the identity: .
Apply it to
We have: .
Multiply by . .
The equation: . has no real roots.
So we have: .
that second solving question has a nice solution, thanks!
I guess I never saw the perfect square trinomial in that first one though
Here's another solution for this one. Originally Posted by Hasan1 2. Previous knowledge: Solution:
The rest follows from Soroban's conclusions.
Originally Posted by Hasan1 2. Just tackle the LHS.
Apply the following identity
The conclusion follows quickly.
Originally Posted by Hasan1 3. The same trick as identity #2, apply
The last one is easy. Expand & observe that (This last identity is a fact that you actually should know.)
And we're done
Is there a way to do those identities without the sum to product formula, but the double angle formula instead?
I think those identities were made to apply the formulae I gave you. It's a quickly way.
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