Question

Which of the following expression expressions is equivalent to cos3x/sinxcosx?

Answer 1

Correct Option:
Option B

Solution:
The given expression is:

$\frac{cos(3x)}{sin(x)cos(x)}$

cos(3x) can be written as cos(2x +x). Expanding it, we get:

$cos(3x) = cos(2x+x) \\ \\ cos(3x) =cos(2x)sin(x)-sin(2x)cos(x)$

Using this value of cos(3x) in given equation, we get:

$\frac{cos(3x)}{sin(x)cos(x)} \\ \\ = \frac{cos(2x)sin(x)-sin(2x)cos(x)}{sin(x)cos(x)} \\ \\ = \frac{cos(2x)sin(x)}{sin(x)cos(x)}- \frac{sin(2x)cos(x)}{sin(x)cos(x)} \\ \\ = \frac{cos(2x)}{cos(x)} - \frac{sin(2x)}{sin(x)} \\ \\ =sec(x)cos(2x)-csc(x)sin(2x)$

Answer 2

Answer:

A.) cscxcos2x-secxsin2x

Step-by-step explanation:

I'm sorry I really do not know how to solve this but I just did the quiz and b was not correct.