Question

Is there anything wrong with this work?
cosθ/2 = √((1 + cosθ)/2)
cosθ = 24/25
cosθ/2 = √(1 + (24/25)/2
cosθ/2 = √((49/25)/2)
cosθ/2 = 7/√50

Answer 1

Then you can optionally rationalize the denominator by multiplying top and bottom by \(\Large \sqrt{50}\)

Answer 2

Keep in mind that \[\Large \sqrt{50} = \sqrt{25*2} = \sqrt{25}*\sqrt{2} = 5\sqrt{2}\]

Answer 3

Nothing else is wrong with it?

Answer 4

Because my teacher didn't give me credit for it

Answer 5

if you rationalize the denominator and use the fact that \[\Large \sqrt{50}=5\sqrt{2}\] then you should get \[\Large \cos\left(\frac{\theta}{2}\right) = \frac{7\sqrt{2}}{10}\]

Answer 6

Ok...thanks!

Answer 7

no problem