Certainly! Let's solve the equation
[tex]\[
(3 - 4 \sin^2 A) \cdot (1 - 3 \tan^2 A) = (3 - \tan^2 A) \cdot (4 \cos^2 A - 3)
\][/tex]
First, we'll work on simplifying both sides of the equation separately.
### Left Side Simplification
The given left side of the equation is:
[tex]\[
(3 - 4 \sin^2 A) \cdot (1 - 3 \tan^2 A)
\][/tex]
### Right Side Simplification
The given right side of the equation is:
[tex]\[
(3 - \tan^2 A) \cdot (4 \cos^2 A - 3)
\][/tex]
### Intermediate Results
By substituting and simplifying the trigonometric identities, we find:
Left Side:
[tex]\[
(4 \sin^2 A - 3) \cdot (3 \tan^2 A - 1)
\][/tex]
Right Side:
[tex]\[
-(4 \cos^2 A - 3) \cdot (\tan^2 A - 3)
\][/tex]
From these intermediate results, you can observe that:
[tex]\[
(4 \sin^2 A - 3)(3 \tan^2 A - 1) \quad \text{and} \quad -(4 \cos^2 A - 3)(\tan^2 A - 3)
\][/tex]
These expressions represent the simplified forms of their respective sides.
### Conclusion
Thus, the given equation simplifies as follows:
[tex]\[
(4 \sin^2 A - 3)(3 \tan^2 A - 1) = -(4 \cos^2 A - 3)(\tan^2 A - 3)
\][/tex]
This demonstrates the relationship between the two sides of the equation after simplification.
