Review the proof of cos(A - B) = cosAcosB + sinAsinB. Which of the following complete step 4 of the proof?

1 and 1
2 and 1
(cosAcosB)2(sinAsinB)2 and (cos2(A – B))((sin2(A – B))
(cos2A + sin2A)(cos2B + sin2B) and (cos2(A – B))(sin2(A – B))

Option (2)

Step-by-step explanation:

Step 1.

Step 2.

(cosA - cosB)² + (sinA - sinB)² = [cos(A - B) - 1]² + [sin(A - B) - 0]²

Step 3.

cos²A + cos²B - 2cosAcosB + sin²A + sin²B - 2sinAsinB  = cos²(A - B) + 1 - 2cos(A - B) + sin²(A - B)

Step 4.

2 - 2cosAcosB - 2sinAsinB = 1 - 2cos(A - B) + 1

Step 5.

cosAcosB + sinAsinB = cos(A - B)

Therefore, Option (2) will be the answer.

the answer is 2 and 1 or B

Step-by-step explanation:

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