A student uses the following steps to prove the sine sum identity. The proof is incorrect.

Step 4 is incorrect ⇒ C

Step-by-step explanation:

Let us check step by step

∵ sin(x + y)

∵ sin(z) = cos( - z)

→ Replace z by (x + y)

∴ sin(x + y) = cos( - [x + y])

∴ Step 2 is correct

∵ cos( - [x + y]) = cos( - x - y])

∵ take [ - x] as the 1st angle and y as the 2nd angle

∴ cos( - x - y]) = cos([ - x] - y)

∴ Step 3 is correct

∵ cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

→ Replace a by ([ - x] and b by y

∴ cos([ - x] - y) = cos( - x)cos(y) + sin( - x)sin(y)

∴ Step 4 is incorrect, the second angle is y not (-y)

∵ cos( - x) = sin(x)

∵ sin( - x) = cos(x)

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

∴ Step 5 is correct

16

step-by-step explanation:

2 x 40 = 80

80/5

= 16

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step-by-step explanation:

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