Question

Find all solutions to the equation
(sinx+cosx)(sinx– cosx)=3.

Answer 1

sin^2-cos^2x=3
(1-cos^2x)-cos^2x=3
1-2cos^2x=3
-2cos^2x=2
cos^2x=-1
no solution

Answer 2

What do you mean no solution?

Answer 3

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)

Answer 4

Because cos(x) can't be an imaginary number. It must be between -1 and +1.

Answer 5

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.