# Homework Help: Help with trig identities

1. Feb 18, 2015

### Marcus27

1. The problem statement, all variables and given/known data
Show that (sin^4 x + (sin^2 x * cos^2 x)) / (cos^2 x - 1) == -1
2. Relevant equations
Sin^2 x + cos^2 x == 1

3. The attempt at a solution
(sin ^4 x + (sin^2 x * cos^2 x)) / (cos^2 x - 1)
= ((sin^2 x)(sin^2 x) + (sin^2 x * cos^2 x)) / (cos^2 x - 1)
=((sin^2 x)(1 - cos^2 x) + (sin^2x * cos^2 x)) / (cos^2 x -1 )
= (sin^2 x - (sin^2 x * cos^2 x) + (sin^2 x * cos^2 x)) / (cos^2 x - 1 )
= (sin^2 x) / (cos^2 x - 1 )
= (1 - cos^2 x ) / (cos^2 x -1)
= -1

I think this is correct, but when I looked up the answer in the back of the textbook it showed completely different working using different substitutions. Did I make any mistakes? or are there two or more solutions to this problem?, if this is the case would I be marked down in an exam for using this method?.

2. Feb 18, 2015

### SteamKing

Staff Emeritus
In working trig identity problems, there may be more than one valid substitution which can be used to obtain a simplification, especially with complicated or lengthy expressions.

If this were an exam exercise, no, you should not be penalized for using a valid method of simplification, even if it differs from a method preferred by the instructor.

3. Feb 18, 2015

### Marcus27

Thanks, that puts my mind at ease.

4. Feb 22, 2015

### HallsofIvy

I, for example, would, seeing that "$sin^4(x)$" change everything else to "sin(x)".
Since $cos^2(x)= 1- sin^2(x)$, the numerator is $sin^4(x)+ sin^2(x)(1- sin^2(x))= sin^4()+ sin^2(x)- sin^4(x)= sin^2(x)$. Is that what your text book does?