Question

Help again...its for math offering 15 points

Answer 1

`\tan \frac{\theta}2 = \frac{1}2`

Step by step Explanation:

`\sin \theta = \frac{\text{Perpendicular} }{\text{Hypotenuse}} = (12)/(15)\\\\\\\cos \theta = \frac{\text{Base}}{\text{Hypotenuse}}= (9)/(15)\\\\\text{Now,}\\\\\tan \frac{\theta}2 = \frac{\sin \tfrac{\theta}2}{\cos \tfrac{\theta}2}\\\\\\~~~~~~~~=\frac{2\cos \tfrac{\theta}2 \sin \tfrac{\theta}2 }{2\cos^2 \tfrac{\theta}2}~~~~~~;\left[\text{Multiply by}~ 2\cos\tfrac{\theta}2 \right]`

`=(\sin \theta)/(1+ \cos \theta)~~~~~~~~~~~~;[2 \sin x \cos x = \sin 2x ~ \text{and}~ 2\cos^2 x =1+\cos 2x]\\\\\\=\frac{\tfrac{12}{15}}{1+ \tfrac{9}{15}}\\\\\\=\frac{\tfrac{12}{15}}{\tfrac{24}{15}}\\\\\\=(12)/(15)* (15)/(24)\\\\\\=(12)/(24)\\\\\\=\frac{1}2`