Using an inductive argument to show that
My attempts so far are:
Step 1. See if it's true for n=1. So,
So LHS = RHS (I think I can say this based on the identity sin2A=2sinAcosA? This is my first issue)
Step 2. Assume it holds true for n = k
Step 3. Show it's true for k+1
Here I know if it is true, then
So taking the LHS
Using index laws
Using sin2A = 2sinAcosA
Now here is where I am confused. I know back in Step 2 I have
and need to substitute this in but I'm unsure how to resolve it to get the answer I know I need!
Hope this all makes sense and that someone can give me a hand. Thanks very much.