Question

Prove that sec^4-cos^4=1-2cos^2 ?

Answer 1

`color(red)"The question is wrong!!!!"`

Explanation:

`color(blue)"Approaching the question on the basis of the information that you have provided, The solution would be:-"`

`sec^4 x - cos^4`

= `(sec^2 x+ cos^2 x)(sec^2 x- cos^2 x)`

= `((1+cos^4 x)(1-cos^4 x))/cos^4 x`

= `(1+cos^4 x)(1-cos^2 x)(1+cos^2 x)/cos^4 x`

`color(blue)"Thus the solution would be not coming equal to RHS"`.

The correct question would be `sin^4x` in place of `sec^4x`.

On solving this question we get,

`sin^4 x - cos^4x = 1 - 2 cos^2 x,` then

LHS = `sin^4 x - cos^4x`

= `(sin^2 x+cos^2 x) (sin^2 x-cos^2 x)`

= `1*(sin^2 x-cos^2 x)`

= `1- cos^2 x - cos^2 x`

= `1 - 2cos^2 x` = RHS