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liubo4ka [24]
3 years ago
15

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

Mathematics
1 answer:
sattari [20]3 years ago
8 0

Answer:

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

Step-by-step 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)

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