1. LHS=2cos 2^a+1/2cos a+1= RHS=(2cos a-1) (2cos 2a-1) (2cos 2^2a-1).....(2cos 2^n-1 a-1)
here a is the angle n is number
we have to prove LHS=RHS
If you're serious about wanting help on this Forum - and, indeed, serious about improving your mathematical skills - you must learn to be more accurate in writing down mathematical expressions. This will save everyone a good deal of time, and help you to acquire the skills you need to solve problems like this.
I think the question is this:Prove, for any positive integer , and any value of , thatThis is done by Mathematical Induction, as follows.
Let be the propositional function:(For convenience, I've swapped the sides of the equation.)
Then, multiplying both sides of the equation by :, using
Now states:The RHS is:So is true. Therefore, by Induction, is true for all positive integers, .