Sin(x-∏/4)= root number 3/2.

Then x-∏/4=∏/3+2k∏ or x-∏/4=2∏/3+2k∏.

So x=7∏/ 12+2k∏ or11∏12+2k ∏.

2)sinx(x+∏/4)= 1/2

X(x+∏/4)=∏/6+2k∏ or 5∏/6+2k∏ There may be something wrong with your topic.

3)asin(x+∏/4)cos(x+∏/4)= a/2 * sin 2(x+∏/4)= a/2 * cos2x = 1

Cos2x=2/a then x=arccos2/a+k∏.

4) f(x) brought by x =-∏/8 should have a plus sign or a minus sign (1+A 2).

That is, the root number 2/2(a- 1)= the square of both sides of the positive and negative root numbers (1+A 2).

Get a =- 1

5) let sin(2arcsin 1/3)=x, then arcsinx=2arcsin 1/3.

Let siny= 1/3, then 2arcsin1/3 = 2y = arcsinx = sin2y, then siny= 1/3.

X= positive or negative (4* root number 2)/9