Use the half-angle formulas to simplify the expression. $- \sqrt { \frac { 1 + \cos 6 x } { 1 - \cos 6 x } }$
A) - |cot x|
B) - |3 tan x|
C) - |3 tan 6x|
D) - |3 cot 3x|
E) - |cot 3x|

Question

Use the half-angle formulas to simplify the expression.   $- \sqrt { \frac { 1 + \cos 6 x } { 1 - \cos 6 x } }$  
A) - |cot x|
B) - |3 tan x|
C) - |3 tan 6x|
D) - |3 cot 3x|
E) - |cot 3x|

Quizplus · Accepted Answer

The expression can be simplified using the half-angle formula for tangent, $\tan \left( \frac{\theta}{2} \right) = \sqrt{ \frac{1 - \cos \theta}{1 + \cos \theta} }$. By applying this to the given expression and considering the negative square root, we get $-|\cot 3x|$, which corresponds to choice E.

Use the Half-Angle Formulas to Simplify the Expression −1+cos⁡6x1−cos⁡6x- \sqrt { \frac { 1 + \cos 6 x } { 1 - \cos 6 x } }−1−cos6x1+cos6x​​

Use the Half-Angle Formulas to Simplify the Expression $- \sqrt { \frac { 1 + \cos 6 x } { 1 - \cos 6 x } }$