Answer: D. [tex]\sqrt{2x^2(1-cos} \beta)[/tex] is the length of b, the side opposite to [tex]\angle B[/tex].
Explanation:
According to the line of cosines, length of one side when opposite angle and two other sides are given.
c^2=a^2+b^2-2 ab cos C, where a,b, c are the sides of triangle while C is the opposite angle of side c.
Here, a=b=x(because [tex]\angle A= \angle C[/tex]) , c= length of b (that is side AC) and [tex]C= \angle B= \beta[/tex]
Thus, [tex]AC^2= x^2+x^2-2x\timesx cos \beta= 2x^2-2x^2cos\beta=2x^2(1-cos\beta) \Rightarrow AC=\sqrt{2x^2(1-cos\beta})[/tex]
Therefore, length of b =[tex]\sqrt{2x^2(1-cos\beta})[/tex]
