Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
tan²x + 1 = sec²x
Consider the left side
[tex]\frac{1+sin^4A}{cos^4A}[/tex]
= [tex]\frac{1}{cos^4A}[/tex] + [tex]\frac{sin^4A}{cos^4A}[/tex]
= [tex]sec^{4}[/tex] A + [tex]tan^{4}[/tex] A
= (tan²A + 1)² + [tex]tan^{4}[/tex] A
= [tex]tan^{4}[/tex] A + 2tan²A + 1 + [tex]tan^{4}[/tex] A
= 1 + 2tan²A + 2[tex]tan^{4}[/tex] A ← factor out 2tan²A
= 1 + 2tan²A(1 + tan²A)
= 1 + 2tan²A sec²A
= right side , thus verified
