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so what i was trying to do here was replace cos2x with the double angle id which is cos^2x-sin^2x

then i factor that and cancle out cosx+sinx

now i have 1/cosx-sinx...so i tried direct sub. and i get 1/sqroot2/2+squroot2/2 which i end up with sqroot 2 but that isn't the right answer

isn't cos 7(pi/4)= squroot 2/2 and sin 7(pi/4)= -squroot2/2?

please show me where i am going wrong