Write the following in terms of cos θ only. cot θ

B)
C)
D)

Question

Write the following in terms of cos  θ  only. cot  θ
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B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

We know that cot θ = cos θ/ sin θ. 
Using the Pythagorean identity, sin^2 θ + cos^2 θ = 1
Rearranging, sin^2 θ = 1 - cos^2 θ 
Substituting in the expression for cot θ: 
cot θ = cos θ / sin θ 
cot θ = cos θ / √(1 - cos^2 θ) 
Simplifying: 
cot θ = cos θ / sqrt(1 - cos^2 θ) 
So cot θ can be expressed solely in terms of cos θ as cot θ = cos θ / sqrt(1 - cos^2 θ). 
Therefore, the best choice is B.

Write the Following in Terms of Cos θ Only