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

O sin(40° – 10°)
O cos(40° + 10º)
O sin(40° + 10º)
O cos(40° – 10º)

1 Answer

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Answer:

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

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)

User Ashok Goli
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