cos^{4} A - sin^{4} A / cos^{2} A - sin^{2} A
= (cos^{2} A)^{2} - (sin^{2}A)^{2} / cos^{2} A - sin^{2} A
= (cos^{2} A + sin^{2}A) (cos^{2} A - sin^{2}A) / (cos^{2} A - sin^{2} A)
= (cos^{2} A + sin^{2}A) (cos^{2} A - sin^{2}A) / (cos^{2} A - sin^{2} A)
= (cos^{2} A + sin^{2}A)
= 1

7sin^{2} x +3cos^{2} x = 4
7sin^{2} x/cos^{2} x + 3cos^{2} x/cos^{2} x = 4/cos^{2} x
7tan^{2} x + 3 = 4sec^{2} x
7tan^{2} x + 3 = 4(1+tan^{2} x)
3tan^{2} x = 1
tan x = 1/√3