Question

sec⁴ A − sec² A is equal to

Options

• tan² A − tan⁴ A

• tan⁴ A − tan² A

• tan⁴ A + tan² A

•  tan² A + tan⁴ A

Answer 1

The given expression is .`sec^4 A-sec^2A`

Taking common `sec^2 A` from both the terms, we have

`Sec^4 A-sec^2 A` 

= `sec^2 A (sec^2 A-1)` 

= `(1+tan^2 A)tan^2 A` 

=`tan^2 A+tan^4 A`