If
cos
2
Acos
2
B
sin
2
A−sin
2
B
​
=x, then the value of x is:

Given identity:
x=
cos
2
Acos
2
B
sin
2
A−sin
2
B
​

We know that sin
2
θ=1−cos
2
θ. Substituting this in the numerator:

sin
2
A−sin
2
B=(1−cos
2
A)−(1−cos
2
B)
sin
2
A−sin
2
B=1−cos
2
A−1+cos
2
B=cos
2
B−cos
2
A
Alternatively, let us split the expression directly by converting it to tangent terms:

x=
cos
2
Acos
2
B
sin
2
A
​
−
cos
2
Acos
2
B
sin
2
B
​

x=tan
2
A⋅
cos
2
B
1
​
−tan
2
B⋅
cos
2
A
1
​

x=tan
2
A(1+tan
2
B)−tan
2
B(1+tan
2
A)
x=tan
2
A+tan
2
Atan
2
B−tan
2
B−tan
2
Btan
2
A
x=tan
2
A−tan
2
B