Question

Given: Cosine (x minus y)

1. = sine (pi/2 - (x minus y))
2. = sine (pi/2 - x + y)
3. = sine ((pi/2 - x) + y )
4. = sine ((pi/2 - x) - (-y))
5. = sine (pi/x - x) cosine (-y) - cosine (pi/2 - x) sine (-y)
6. = cosine (x) cosine (-y) - sine (x) sine (-y)
7. = cosine (X) cosine (y) + sine (x) sine (y)
Choose a justification for each step in the derivation of the sine difference identity.

Step 1:

Step 2: Distributive property

Step 3: Associative property

Step 4: Factoring out –1

Step 5:

Step 6:

Step 7:

Answer 1

Step 1- cofunction identity

Step 5- sine difference identity

Step 6- cofunction identity

Step 7- cosine function is even, some is odd

Explanation:

edge2020