First, notice that:
![2\tan (\frac{x}{2})=2\cdot(\pm\sqrt[]{\frac{1-cosx}{1+\cos x})}](https://tex.z-dn.net/?f=2%5Ctan%20%28%5Cfrac%7Bx%7D%7B2%7D%29%3D2%5Ccdot%28%5Cpm%5Csqrt%5B%5D%7B%5Cfrac%7B1-cosx%7D%7B1%2B%5Ccos%20x%7D%29%7D)
And in the denominator we have:
then, we have on the original expression:
![\begin{gathered} \frac{2\tan(\frac{x}{2})}{1+\tan^2(\frac{x}{2})}=\frac{2\cdot\pm\sqrt[]{\frac{1-\cos x}{1+cosx}}}{\frac{2}{1+\cos x}}=\frac{2\cdot(\pm\sqrt[]{1-cosx})\cdot(1+\cos x)}{2\cdot(\sqrt[]{1+cosx})} \\ =(\sqrt[]{1-\cos x})\cdot(\sqrt[]{1+\cos x})=\sqrt[]{(1-\cos x)(1+\cos x)} \\ =\sqrt[]{1-\cos^2x}=\sqrt[]{\sin^2x}=\sin x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B2%5Ctan%28%5Cfrac%7Bx%7D%7B2%7D%29%7D%7B1%2B%5Ctan%5E2%28%5Cfrac%7Bx%7D%7B2%7D%29%7D%3D%5Cfrac%7B2%5Ccdot%5Cpm%5Csqrt%5B%5D%7B%5Cfrac%7B1-%5Ccos%20x%7D%7B1%2Bcosx%7D%7D%7D%7B%5Cfrac%7B2%7D%7B1%2B%5Ccos%20x%7D%7D%3D%5Cfrac%7B2%5Ccdot%28%5Cpm%5Csqrt%5B%5D%7B1-cosx%7D%29%5Ccdot%281%2B%5Ccos%20x%29%7D%7B2%5Ccdot%28%5Csqrt%5B%5D%7B1%2Bcosx%7D%29%7D%20%5C%5C%20%3D%28%5Csqrt%5B%5D%7B1-%5Ccos%20x%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B1%2B%5Ccos%20x%7D%29%3D%5Csqrt%5B%5D%7B%281-%5Ccos%20x%29%281%2B%5Ccos%20x%29%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B1-%5Ccos%5E2x%7D%3D%5Csqrt%5B%5D%7B%5Csin%5E2x%7D%3D%5Csin%20x%20%5Cend%7Bgathered%7D)
therefore, the identity equals to sinx
Answer:
On a calculator you would get 120.008264463
other wise know as 120 1/121
Answer:
3/7
Step-by-step explanation:
its 3/7 because there are 3 weekend days and there are 7 days in total in one week, so out of the week there is 3 weekend days.
i hope this helps :)
Answer:
about $2,557
Actual cost : $2556.97
Step-by-step explanation:
well since all of them are .99 if you round to the hundreths it make another dollar cause it will force the .9 to become 1.0
so it be 1450 for the refrigerator, 490 for the dishwasher, and 617 for the electric range.
add those numbers to get about $2,557
Answer:
3,8
Step-by-step explanation:
