Question

Given:

A. sin(x)

B. cos(x)

C. cos(y)

D. sin(y)

Use the drop-down menus in the derivation of the sine sum identity:

sin(x + y)

= cos (StartFraction pi Over 2 EndFraction minus (x + y))

= Cosine ((StartFraction pi over 2 EndFraction minus x) minus y)

= Cosine (StartFraction pi Over 2 EndFraction minus x)
A
+ Sine (StartFraction pi Over 2 EndFraction minus x)
A

sin(x)cos(y) + cos(x)sin(y)

Answer 1

The sine sum identity, sin(x + y) = sin(x)cos(y) + cos(x)sin(y), can be derived by utilizing the cosine function and making progressive substitutions.

Step-by-step explanation:

The given question is asking for the derivation of the sine sum identity using the given trigonometric functions. The sine sum identity is given by:

sin(x + y) = sin(x)cos(y) + cos(x)sin(y)

To derive this identity, we can use the cosine function to rewrite the expression:

1. sin(x + y) = cos(π/2 - (x + y))
2. sin(x + y) = cos(π/2 - x - y)
3. sin(x + y) = cos(π/2 - x)cos(y) + sin(π/2 - x)sin(y)
4. sin(x + y) = cos(π/2 - x)sin(y) + sin(π/2 - x)cos(y)

Answer 2

C, D

Step-by-step explanation: