Question

Solve the following equation for
0 less than and/or equal to "x" less than and/or equal to 360

--
cos^2x - 1 = sin^2x
--

Attempt:
cos^2x - 1 - sin^2x = 0
cos^2x - 1 - (1 - cos^2x) = 0
cos^2x - 1 - 1 + cos^2x = 0
2cos^2x - 2 = 0
(2cos^2x/2)= (-2/2)
cos^2x = -1
cosx = square root of -1

And I can't do anything with this now...what am I doing wrong?


--
Textbook answers:

0, 180, 360
--

Answer 1

On the fourth/fifth line, you erred. When you add 2 to both sides, the right side is positive, not negative.

cos^2 x=1
cos x= +- 1
giving 1, 180,360