Following are the solution to the given expression:
Given:
[tex]0< x< \frac{\pi}{2}\\\\\frac{\sin \frac{x}{2} \tan \frac{x}{2}}{1-\cos x}[/tex]
To find:
value=?
Solution:
[tex]0< x< \frac{\pi}{2}\\\\ \to \frac{\sin \frac{x}{2} \tan \frac{x}{2}}{1-\cos x}[/tex]
Let [tex]x= \frac{\pi}{2}[/tex]
[tex]\to \frac{\sin \frac{\pi}{4} \tan \frac{\pi}{2}}{1-\cos \frac{\pi}{2}}\\\\\to \frac{\frac{1}{\sqrt{2}} \times 1 }{1-0}\\\\\to \frac{\frac{1}{\sqrt{2}} }{1}\\\\\to \frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}\\\\\to \frac{\sqrt{2}}{2}[/tex]
Therefore, the answer is "[tex]\frac{\sqrt{2}}{2}[/tex]".
Learn more:
brainly.com/question/19920270
