Exercise 4 Page 963

We want to verify the given trigonometric identity. sec θ sin θ cot θ =1 We will start on the left-hand side and use Trigonometric Identities to arrive at the right-hand side. 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

Substitute

sec θ= 1/cos θ

1/cos θ sin θ cot θ

MoveRightFacToNumOne

1/b* a = a/b

sin θ/cos θ cot θ

Now we will use one of the Cotangent Identities. 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

Substitute

cot θ= cos θ/sin θ

sin θ/cos θ ( cos θ/sin θ )

MultFrac

Multiply fractions

sin θ cos θ/cos θ sin θ

CommutativePropMult

Commutative Property of Multiplication

sin θ cos θ/sin θ cos θ

QuotOne

a/a=1

1 ✓

We started on the left-hand side of the identity and used Trigonometric Identities to arrive at the right-hand side. Therefore, we have verified the identity.