Answer:
Undefined
Step-by-step explanation:
An expression in mathematics which does not have meaning and so which is not assigned an interpretation. For example, division by zero is undefined in the field of real numbers.
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:
5 times 3 =15lb
Step-by-step explanation:
<span>Assuming the graph is y=-3(√2x)-4 and y=-3√(x-4) the transformation would be:
</span><span>The graph is compressed horizontally by a factor of 2
x=1/2x'
</span>y=-3(√2x)-4
y=-3(√x')-4 <span>
</span><span>moved left 4
x=x'-4
</span>y=-3(√x)-4
y=-3(√x'-4)-4
<span>
moved down 4
y=y'-4
</span>y=-3(√x-4)-4
y'-4=-3(√x'-4)-4
y'=-3(√x'-4)-4 +4
y'=-3(√x'-4)
Answer: C. <span>The graph is compressed horizontally by a factor of 2, moved left 4, and moved down 4.
</span>
