Question

What is the simplest form of the expression below?

StartFraction cotangent (theta) cosine (theta) Over sine (theta) EndFraction times tangent (theta) divided by StartFraction sine (theta) Over cosine (theta) tangent (theta) EndFraction

sec Theta

cot Theta

csc Theta

tan Theta

Answer 1

cot Theta

Explanation:

The answer and comment above is correct.

Answer 2

(B) cot Theta

Explanation:

We want to simplify the expression:

`(cot\theta cos\theta)/(sin\theta ) X(tan\theta)/((sin\theta)/(cos\theta tan \theta) )`

Now:

`( cos\theta)/(sin\theta ) =cot\theta\\( sin\theta)/(cos\theta )=tan \theta\\$Substituting these into the expression\\(cot\theta cos\theta)/(sin\theta ) X(tan\theta)/((sin\theta)/(cos\theta tan \theta) )=cot\theta cot\theta X(tan\theta)/((tan\theta)/( tan \theta) )\\=cot\theta cot\theta X tan\theta$ (Since cot\theta X tan\theta =1) \\$Therefore our result:\\=cot\theta`