Possible values of p for a triangle with given angle A=45 and tanBtanC=p

[zorro]

Homework Statement

Let A,B,C be three angles such that A=45 (degrees) and tanBtanC=p. Find all possible values of p such that A,B,C are the angles of a triangle.

Homework Equations

The Attempt at a Solution

I got an expression for cos(B-C)= (1+p)/{(p-1)√2}
My book says this-
Since B or C can vary from 0 to 135,
-1/√2 < (1+p)/{(p-1)√2} <= 1

I did not understand how this step came. Please help

 

[vela]

Hint: You know that B+C=135, so B=135-C and B-C=135-2C.

 

[zorro]

But B-C=135-2C is not independent of C.
How will that help?

 

[vela]

Why should it be independent of C? Think about what range of values C can assume and what this means about range of values cos(B-C) can assume.

 

[zorro]

Thanks, I got it