Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
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Exercise 3 Page 963

Recall the Trigonometric Identities. Start by using the Reciprocal Identity cot θ = 1tan θ.

csc^2 θ

Practice makes perfect

First, let's recall one of the Reciprocal Identities. Note that we will need to rearrange the terms so that we can use it for our expression. cot θ = 1/tan θ ⇔ 1/cot θ = tan θ With this identity we can substitute 1cot θ for tan θ in our expression.

cot θ ( tan θ + cot θ )
cot θ ( 1/cot θ + cot θ )
cot θ * 1/cot θ + cot^2 θ
cot θ/cot θ + cot^2 θ
1 + cot^2 θ

Now we will use one of the Pythagorean Identities. 1 + cot^2 θ = csc^2 θ With this identity we can substitute csc^2 θ for 1 + cot^2 θ in our expression.

1 + cot^2 θ
csc^2 θ

We have simplified the given expression. cot θ ( tan θ + cot θ ) = csc^2 θ