Exercise 6 Page 963

We want to verify the given trigonometric identity. sec θ cot θ =csc θ We will start on the left-hand side and use Trigonometric Identities to arrive at the right-hand side. First, let's recall the Cotangent Identity. cot θ = cos θ/sin θWith this identity we can substitute cos θsin θ for cot θ in our expression.

sec θ cot θ

Substitute

cot θ= cos θ/sin θ

sec θ * cos θ/sin θ

MoveLeftFacToNum

a*b/c= a* b/c

sec θ cos θ/sin θ

Now we will use 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 cos θ/sin θ

Substitute

sec θ= 1/cos θ

1cos θ * cos θ/sin θ

FracMultDenomToNumber

a/cos θ* cos θ = a

1/sin θ

Finally, let's apply another Reciprocal Identity. csc θ = 1/sin θ With this identity, we can substitute csc θ for 1sin θ in our expression.

1/sin θ

Substitute

1/sin θ= csc θ

csc θ ✓

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.