Question

What is the simplest form of the expression below?

Answer 1

Answer:

B

Step-by-step explanation:

cot theta

Answer 2

Answer:

(B) cot Theta

Step-by-step explanation:

We want to simplify the expression:

$\dfrac{cot\theta cos\theta}{sin\theta } X\dfrac{tan\theta}{\frac{sin\theta}{cos\theta tan \theta} }$

Now:

$\dfrac{ cos\theta}{sin\theta } =cot\theta\\\dfrac{ sin\theta}{cos\theta }=tan \theta\\ Substituting these into the expression\\\dfrac{cot\theta cos\theta}{sin\theta } X\dfrac{tan\theta}{\frac{sin\theta}{cos\theta tan \theta} }=cot\theta cot\theta X\dfrac{tan\theta}{\frac{tan\theta}{ tan \theta} }\\=cot\theta cot\theta X tan\theta (Since cot\theta X tan\theta =1) \\ Therefore our result:\\=cot\theta$