Please type this as 2(sin 2x)^2=2 <span>2sin^2 2x=2 is confusing.
Reducing this expression: (sin 2x)^2 = 1
Taking the sqrt of both sides, sin 2x = plus or minus 1
If sin 2x = 1, then 2x must be pi/2 or 3pi/2, and so x must be pi/4 or 3pi/4.
Now you do this for sin 2x = -1.</span>
The answer to this rests on knowing that there are four properties of multiplication (which your teacher will likely expect you to know...):
These are:
1. commutative
2. associative
3. multiplicative identity
4. distributive
I won't define each of these -- they should be in your notes or textbook. Look them up.
In this case, we are multiplying three terms together -- on the left hand side the parentheses mean to multiply a and b first, then multiply that by 3. On the right hand side, we multiply b times 3 first, and then multiply the product by a.
This would be an example of the associative property of multiplication: when three or more factors are multiplied together, the product is the same regardless of how the factors are grouped.
Hope this helps!
Good luck
let's firstly conver the mixed fractions to improper fractions and then get their product.
![\stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}} ~\hfill \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9}{2}\cdot \cfrac{5}{2}\cdot 6\implies \cfrac{270}{2}\implies 135](https://tex.z-dn.net/?f=%5Cstackrel%7Bmixed%7D%7B4%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B4%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B9%7D%7B2%7D%7D%20~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B2%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B5%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B9%7D%7B2%7D%5Ccdot%20%5Ccfrac%7B5%7D%7B2%7D%5Ccdot%206%5Cimplies%20%5Ccfrac%7B270%7D%7B2%7D%5Cimplies%20135)
hmmm I take it that one can write that mixed as 
.
is valid, not that it makes any sense.
So, I think that your answer will be D because it has to end at a degree of 180
