Which of the following expressions is equivalent to the given expression $\sqrt { \frac { 25 - 25 \cos \theta } { 1 + \cos \theta } }$ ?
($\theta $ $\neq$ $\pi$n, where n is a whole number)
A) $\frac { 1 - \cos \theta } { | \sin \theta | }$
B) $\frac { 5 - 5 \cos \theta } { | \sin \theta | }$
C) $\frac { 5 + 5 \sin \theta } { | \cos \theta | }$
D) $\frac { 5 - 5 \sin \theta } { | \cos \theta | }$
E) $\frac { 5 + 5 \cos \theta } { | \sin \theta | }$

Question

Which of the following expressions is equivalent to the given expression $\sqrt { \frac { 25 - 25 \cos \theta } { 1 + \cos \theta } }$ ? 
($\theta $  $\neq$ $\pi$n, where n is a whole number)  
A) $\frac { 1 - \cos \theta } { | \sin \theta | }$
B) $\frac { 5 - 5 \cos \theta } { | \sin \theta | }$
C) $\frac { 5 + 5 \sin \theta } { | \cos \theta | }$
D) $\frac { 5 - 5 \sin \theta } { | \cos \theta | }$
E) $\frac { 5 + 5 \cos \theta } { | \sin \theta | }$

Quizplus · Accepted Answer

The given expression can be simplified using trigonometric identities. First, factor out 25 from the numerator to get $25(1 - \cos \theta)$. Recognize that $1 - \cos \theta = 2\sin^2(\frac{\theta}{2})$ and $1 + \cos \theta = 2\cos^2(\frac{\theta}{2})$. Substituting these identities and simplifying gives $\sqrt{\frac{25 \cdot 2\sin^2(\frac{\theta}{2})}{2\cos^2(\frac{\theta}{2})}}$, which simplifies further to $\frac{5\sin(\frac{\theta}{2})}{\cos(\frac{\theta}{2})}$, or $\frac{5 - 5\cos \theta}{|\sin \theta|}$, matching choice B.

Which of the Following Expressions Is Equivalent to the Given 25−25cos⁡θ1+cos⁡θ\sqrt { \frac { 25 - 25 \cos \theta } { 1 + \cos \theta } }1+cosθ25−25cosθ​​

Which of the Following Expressions Is Equivalent to the Given $\sqrt { \frac { 25 - 25 \cos \theta } { 1 + \cos \theta } }$