Induction in Trigonometric Proofs
Proving trigonometric identities using induction follows the usual route. The identity usually involves summing a trigonometric series or simplifying a product.
1. Define the identity to be proved so that the statement is equivalent to 'is true'.
2. Prove the identity fororto show that the statementoris true.
3. Assuming the statementis true, prove the statement
Example: Use induction to prove the identity
Ifthe identity becomes
Suppose then thatis true so that(1)
is the statement that
Addingto both sides of (1) gives
Concentrate on the left hand side.
(2) becomesso P(k+1) is proved.