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vazorg [7]
4 years ago
12

Sin^2(x/2)=sin^2x Find the value of x

Mathematics
1 answer:
Veronika [31]4 years ago
6 0
\sin^2\dfrac x2=\sin^2x
\dfrac{1-\cos x}2=1-\cos^2x
1-\cos x=2-2\cos^2x
2\cos^2x-\cos x-1=0
(2\cos x+1)(\cos x-1)=0
\implies\begin{cases}2\cos x+1=0\\\cos x-1=0\end{cases}\implies\begin{cases}\cos x=-\frac12\\\cos x=1\end{cases}

The first case occurs in 0\le x for x=\dfrac{2\pi}3 and x=\dfrac{4\pi}3. Extending the domain to account for all real x, we have this happening for x=\dfrac{2\pi}3+2n\pi and \dfrac{4\pi}3+2n\pi, where n\in\mathbb Z.

The second case occurs in 0\le x when x=0, and extending to all reals we have x=2n\pi for n\in\mathbb Z, i.e. any even multiple of \pi.
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pshichka [43]

Hello from MrBillDoesMath!

Answer:

=   (the equal sign)


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The distance between the cities is 280 miles. The rule is y = 40x, where x is the distance in inches on the map and y is the distance in miles.

Step-by-step explanation:

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The map's key shows that 5 inches on the map equal 200 miles of actual distance.

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if we divide both sides by 5, we get;

1 inch on the map = 40 miles of actual distance.

Step 2:

If x is the distance on the map in inches and y is the actual distance in miles,

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