Question

Sum, Difference, and Cofunction Identities: Mastery Test. Drag each label to the correct location on the expression. Complete this equation: sin(θ) + sin(θ - y) = ?

A. tan(θ)
B. sin(2θ)
C. cot(y)
D. cos(θ)

Answer 1

To solve the given equation sin(θ) + sin(θ - y) = ?, we can use the sum identity for sine. By substituting the values into the sum identity, simplifying further, we get 2sin((2θ - y)/2)cos(y/2).

Step-by-step explanation:

The given equation is sin(θ) + sin(θ - y) = ?

To solve this equation, we can use the sum identity for sine:

sin(a) + sin(b) = 2sin((a + b)/2)cos((a - b)/2)

Comparing this with the given equation, we can see that a = θ and b = θ - y.

So, substituting the values into the sum identity, we get:

sin(θ) + sin(θ - y) = 2sin((θ + (θ - y))/2)cos((θ - (θ - y))/2)

Simplifying further, we have:

sin(θ) + sin(θ - y) = 2sin((2θ - y)/2)cos(y/2)

Therefore, the equation is equal to 2sin((2θ - y)/2)cos(y/2).