Question

Sin^4 A - cos^4 A/sin^2 A - cos^2 A = 1

Answer 1

$sin^4A-cos^4A=(sin^2A)^2-(cos^2A)^2$

Let $sin^2A=a\\cos^2A=b$

Then, [tex]sin^4A-cos^4B\\=a^2-b^2\\=(a+b)(a-b)\\ =(sin^2A+cos^2A)(sin^2A-cos^2A)[/tex]

[tex] \frac{sin^4 A-cos^4 A}{sin^2 A-cos^2 A}= \frac{(sin^2A+cos^2A)(sin^2A-cos^2 A)}{sin^2A-cos^2A} =sin^2A+cos^2 A=1 [/tex]