Question

Which expression is equivalent to cos(40°)cos(10") + sin(40°)sin(10º)?

Answer 1

Answer:

The equivalent expression is cos(40° – 10º) ⇒ D

Step-by-step explanation:

The rule of cosine the compound angles is

cos (A + B) = cos A cos B - sin A sin B

cos (A - B) = cos A cos B + sin A sin B

Let us use these rules to solve the question

∵ cos(40°)cos(10°) + sin(40°)sin(10º)

∵ The middle sign is plus

∴ We will use the 2nd rule above

→ Compare the rule by the given expression to find the value of A and B

∵ A = 40° and B = 10°

∴ cos (A - B) = cos (40° - 10°)

∴ cos (40° - 10°) = cos(40°)cos(10°) + sin(40°)sin(10º)

∴ The equivalent expression is cos(40° – 10º)