Exercise 2 Page 963

Use the Reciprocal Identity sec θ = 1cos θ and Cotangent Identity cot θ = cos θsin θ.

Practice makes perfect

First, let's recall one of the Reciprocal Identities. sec θ = 1/cos θ With this identity we can substitute 1cos θ for sec θ in our expression.

sec θ sin θ cot θ

sec θ= 1/cos θ

1/cos θ * sin θ cot θ

1/b* a = a/b

sin θ/cos θ * cot θ

Now we will use the Cotangent Identity. cot θ = cos θ/sin θ With this identity, we can substitute cos θsin θ for cot θ in our expression.

sin θ/cos θ * cot θ

cot θ= cos θ/sin θ

sin θ/cos θ ( cos θ/sin θ )

Multiply fractions

sin θ cos θ/cos θ sin θ

Commutative Property of Multiplication

sin θ cos θ/sin θ cos θ

a/a=1

We have simplified the given expression. sec θ sin θ cot θ = 1

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