anonymous
  • anonymous
Find all solutions to the equation (sinx+cosx)(sinx– cosx)=3.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
sin^2-cos^2x=3 (1-cos^2x)-cos^2x=3 1-2cos^2x=3 -2cos^2x=2 cos^2x=-1 no solution
anonymous
  • anonymous
What do you mean no solution?
anonymous
  • anonymous
sin^2-cos^2x=3 (1-cos^2x)-cos^2x=3 1-2cos^2x=3 -2cos^2x=2 cos^2x=-1 no solution (refer 0)

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anonymous
  • anonymous
Because cos(x) can't be an imaginary number. It must be between -1 and +1.
anonymous
  • anonymous
Alternate method, maybe less painful.\[3=(sinx+cosx)(sinx– cosx)=\sin^2x-\cos^2x \le \sin^2x+\cos^2x=1\]Contradiction (3 is not less than one) implies no solution. Nothing wrong with methods above, just thought I would put a slightly different method into the discussion.

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