Chapter Test
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Recall the Trigonometric Identities. Start by using the Reciprocal Identity cot θ = 1tan θ.
csc^2 θ
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.
tan θ= 1/cot θ
Distribute cot θ
a* 1/b= a/b
a/a=1
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.
We have simplified the given expression. cot θ ( tan θ + cot θ ) = csc^2 θ