## 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

sois true.

Suppose then thatis true so that(1)

is the statement that

Addingto both sides of (1) gives

Concentrate on the left hand side.

(2)

Usewithandto obtain

(2) becomesso P(k+1) is proved.