Question

Question #1d49a

Answer 1

Have a look to the answer...

Explanation:

Let's start with LHS...

LHS

`sec^4x-tan^2x`
`=(sec^2x)^2-tan^2x`
`=(1+tan^2x)^2-tan^2x` [w.r.t the trigo... identity]
`=tan^4x+2tan^2x+1-tan^2x`
`=tan^4x+(tan^2x+1)`
`=tan^4x+sec^2x` [As per trigo...identity]
`=RHS`

PROVED

Hope it helps...
Thank you...

Answer 2

see below

Explanation:

we will need the identity

`color(red)(1+tan^2x=sec^2x)`

we have to prove

`sec^4x-tan^2x=tan^4x+sec^2x`

`LHS=sec^4x-tan^2x=(color(red)(1+tan^2x))^2-tan^2x`

`=1+2tan^2x+tan^4x-tan^2x`

`=color(red)(1+tan^2x)+tan^4x`

`=sec^2x+tan^4x=tan^4x+sec^2x=RHS`

Answer 3

https://socratic.org/s/aK4viQUb