Which of the following expressions is equivalent to the given expression $$\sqrt { \frac { 25 - 25 \cos \theta } { 1 + \cos \theta } }$$ ? (? ? ?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

Quizplus · Accepted Answer

The given expression can be simplified using trigonometric identities. Factor out 25 from the numerator to get $\sqrt{\frac{25(1-\cos\theta)}{1+\cos\theta}}$. Recognize the numerator and denominator as part of the trigonometric identity $\sin^2\theta = 1 - \cos^2\theta$, and simplify to get $\frac{5\sqrt{1-\cos\theta}}{\sqrt{1+\cos\theta}}$. Further simplification using the identity $\sin^2\theta = 1 - \cos^2\theta$ and the Pythagorean identity leads to $\frac{5(1-\cos\theta)}{|\sin\theta|}$, which matches 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 $\sqrt { \frac { 25 - 25 \cos \theta } { 1 + \cos \theta } }$