Sin^4x+2cos^2x-cos^4=1

Proven .  We are done proving this identity because we get a true statement, which is  1 = 1.

Step-by-step explanation:

Sin^4x+2cos^2x-cos^4=1

...

We want to prove : (Sin x ) ^ 4   +   2  (cos x)^2   -   (cos x)^4   =    1  

(Sin x ) ^ 4   +   2  (cos x)^2   -   (cos x)^4   =    1  

Factor this trinomial.  considering  ((cos x)^2) is the variable

so

( ((sin x)^2) ^2  -  ( (cos x)^2)^2   +   2 (cos x)^2   +  1  - 1   = 1

( ((sin x)^2) ^2  -  ( (cos x)^2)^2   +   2 (cos x)^2   - 1   +  1   = 1

( ((sin x)^2) ^2   + [-  ( (cos x)^2)^2   +   2 (cos x)^2   - 1 ]  +  1   = 1

( ((sin x)^2) ^2   -  [  ( (cos x)^2) - 1 ]^2  +  1   = 1

But also notice that  (sin x)^2  =  1  -  (cos x)^2  from the trig identity:

 (sin x)^2  +  (cos x)^2 =  1  

( (1  -  (cos x)^2) ^2   -  [  ( (cos x)^2) - 1 ]^2  +  1   = 1

here we see that   (1  -  (cos x)^2) ^2  =  [  ( (cos x)^2) - 1 ]^2

so  we  get     ( 0     +  1) = 1

 1 = 1   true.

Proven .  We are done proving this identity because we get a true statement.

a) justify

step-by-step explanation:

justifying is just part of everyday life. justify kind of means proof so i think the answer is a) justify.