Question

B)
1 + sin^4A ÷cos^4A = 1 + 2tan^2A.sec^2A
​

Answer 1

see explanation

Explanation:

Using the trigonometric identity

tan²x + 1 = sec²x

Consider the left side

`(1+sin^4A)/(cos^4A)`

=
`(1)/(cos^4A)` +
`(sin^4A)/(cos^4A)`

=
`sec^(4)` A +
`tan^(4)` A

= (tan²A + 1)² +
`tan^(4)` A

=
`tan^(4)` A + 2tan²A + 1 +
`tan^(4)` A

= 1 + 2tan²A + 2
`tan^(4)` A ← factor out 2tan²A

= 1 + 2tan²A(1 + tan²A)

= 1 + 2tan²A sec²A

= right side , thus verified