Question

Write the expression as either the sine, cosine, or tangent of a single angle. (2 points)

cosine of pi divided by three times cosine of pi divided by five plus sine of pi divided by three times sine of pi divided by five.

Answer 1

cos(π/3)cos(π/5) + sin(π/3)sin(π/5) = cos(2π/15)

Explanation:

We will make use of trig identities to solve this. Here are some common trig identities.

Cos (A + B) = cosAcosB – sinAsinB

Cos (A – B) = cosAcosB + sinAsinB

Sin (A + B) = sinAcosB + sinBcosA

Sin (A – B) = sinAcosB – sinBcosA

Given cos(π/3)cos(π/5) + sin(π/3)sin(π/5) if we let A = π/3 and B = π/5, it reduces to

cosAcosB + sinAsinB and we know that

cosAcosB + sinAsinB = cos(A – B). Therefore,

cos(π/3)cos(π/5) + sin(π/3)sin(π/5) = cos(π/3 – π/5) = cos(2π/15)