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:
Floor ride up to = 13 floor
Step-by-step explanation:
Given:
Parking garage = 4 floors under ground
Elevator up-to = 17 floor
Find:
Floor ride up to
Computation:
Floor ride up to = Elevator up-to - Parking garage
Floor ride up to = 17 floor - 4 floor
Floor ride up to = 13 floor
Rectangle ABCD was rotated 90° counterclockwise around the origin and then translated 8 units down.
Answer:
277°
Step-by-step explanation:
The measure of arc AEG = AB + BE + EF + FG
The central angle is congruent to the arc that subtends it
∠ ECB = 180° - 44° = 136° ( adjacent angles )
∠ECF = ∠ ACB = 44° ( vertical angles ), thus
AEG = 44° + 136° + 44° + 53° = 277°
Answer:
its D Please put me as brain eat if correct
