SOLUTION: sinx + cosx - sinxcosx = sin^2 x + cos^2 x

Question 94923: sinx + cosx - sinxcosx = sin^2 x + cos^2 x
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
sinx + cosx - sinxcosx = sin^2 x + cos^2 x
cosx + sinx - sinxcosx = 1
cosx + sinx = 1 + sinxcosx
cos^2 x + 2cosxsinx + sin^2 x = 1 + 2sinxcosx + sin^2 x cos^2 x
cos^2 x + sin^2 x = 1 + sin^2 x cos^2 x
1 = 1 + sin^2 x cos^2 x
0 = sin^2 x cos^2 x
sin^2 x = 0
Ans: 2(pi)k
cos^2 x = 0
Ans: (pi)/2 + 2(pi)k
~k is any integer

RELATED QUESTIONS
simplify: SIN^2 x - COS^2 x/SINX +... (answered by lwsshak3)

prove that... (answered by MathLover1)

((sinx+cosx)/((tan^2(x))-1))=((cos^2(x)/(sin(x)-cos(x) (answered by Alan3354)

Simplify (1-cos^2 x)/ sinx * cosx (answered by lwsshak3)

solve sin^2 x + (sinx)(cosx) =... (answered by Alan3354)

Find an equivalent expression for cos 3x in terms of powers of cos x. cos 3x = cos (2x (answered by eggsarecool)

prove 2cot2xcosx=cscx-2sinx I tried starting on the left. My work is... (answered by addingup)

Prove using reciprocal and pythagorean identities: (cscx-cotx)/(secx-1)= cotx I have... (answered by jsmallt9)

how do you prove that sinxCosx=cosx-cos^3x/sinx are egual? also 2+2Cot^2= 2cotx secx... (answered by Fombitz)