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**1. The problem statement, all variables and given/known data**

I have to trig problems which I'm not entirely sure how to approach:

1) For which angles x is (sinx)^4-(cosx)^4 > (sinx)^2-(cosx)^2?

2) For what value x is the expression (sinx-cosx)^2+(sinx+cosx)^2 as large as possible?

**3. The attempt at a solution**

For the first one I was able to add and subtract 1 to the left side which gave me a difference of squares that let me use the pythagorean identity leaving me with sinx^2-cosx^2>sinx^2_cosx^2 But this doesn't really make sense, so I'm not sure where to go.

For the second, am I supposed to do this numerically? or how would I approach it analytically?

Thanks for the help.