Answer both and explain please

1. Prove the following trigonometric identity: [3] 2 tan x sin 2x = 1 + tan' x Clearly label or explain each trig identity as you use them. 2. In this questions we will investigate some patterns in where p is a prime and 0 S k s p. [4] a) Evaluate each of (. () (). () and identify which values are divisibly by 3. b) Evaluate each of (3). (5). (5). (5). (5). () and identify which values are divisibly by 5. c) If p is a prime, predict which of will be divisible by p and which will not. d) Using the formula for () and properties of prime numbers, explain why the pattern you identified in c) should always occur for any prime p