SOLUTION: I am asked to multiply, then use fundamental identities to Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not eq

Algebra ->  Trigonometry-basics -> SOLUTION: I am asked to multiply, then use fundamental identities to Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not eq      Log On


   

Question 829191: I am asked to multiply, then use fundamental identities to Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.
The expression is: (sin x + cos x)(sin x - cos x)
The following I need to compare it to to see which ONE is not equivalent are:
1 - 2cos^(2)x
csc^(2)x - cot^(2)x - 2cos^(2)x
sin^(2)x - cos^(2)x
2sin^(2)x - sec^(2)x - tan^(2)x
1 - 2sin ((pi/2) - x) cos x
If you could please include the steps you used to get your answer as well would be most helpful for me.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The expression is: (sin x + cos x)(sin x - cos x)
Use FOIL to get:
= sin^2(x)-cos^2(x)
= (1-cos^2(x)-cos^(x))
= 1 - 2cos^2(x)
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The following I need to compare it to to see which ONE is not equivalent are:
1 - 2cos^(2)x::: yes
--------
csc^(2)x - cot^(2)x - 2cos^(2)x:: ?
=(csc^2(x)-cos^2(x)) - 2cos^2(x)
= 1 - 2cos^2(x)
So::: yes
------------------------------
sin^(2)x - cos^(2)x::: yes
2sin^(2)x - sec^(2)x - tan^(2)x:: ?
= 2sin^2(x)-(sec^2x)-tan^2(x))
= 2sin^2(x)-1
So::: no
------------------------------
1 - 2sin ((pi/2) - x) cos x::: yes
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Cheers,
Stan H.
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