HW: p.488 # 4,6,8,13,14,15,16,20 Aim: How do we prove trig identities? Do Now: 1. Rewrite (tan A)(csc A) in terms of sin A, cos A or both. 2. Add: HW: p.488 # 4,6,8,13,14,15,16,20

(tan A)(csc A) = sec A. this is called trig identity. An identity is an equation whose solution set is the set of all possible replacements of the variable for which each member of the equation is defined.

can be written as cot x + tan x, and = Notice that can be written as cot x + tan x, and can be written as Therefore, cot x + tan x = is one of the trig identity.

To prove a trig identity we can work from either side of equation, and sometimes we need to work on both sides of the equation in order to make both sides balanced. Very often we need to change other trig functions into sin, cos or both functions to start.

To prove this, we need to rewrite both cos 2θ and sin 2θ by their identities

Prove: On the right side, we try to cancel sec2 θ, then we use the identity cos θ and sec θ are reciprocal to each other, therefore

Which of the following is equivalent to b) c) d)

Prove the following trig. identities 1. 2. 3. 4. 5.