Find all solutions in the interval [0, 2π).

sin^2(x) - cos^2(x) = 0

Question

Find all solutions in the interval [0, 2π). 

sin^2(x) - cos^2(x) = 0

anonymous · Answer

guys help me out!!!:(

tkhunny · Answer

You could factor the difference of squares.

Youcoul duse the pythagorean Identity to convert cosine to same expression with sine.

You may wish to ponder $\cos(2x)$.

Lot's of ways to go about it.

anonymous · Answer

@tkhunny so x=pi/4, 3pi/4 right?? are there anymore?

anonymous · Answer

Yeah that's right. If you factor it as a difference of squares, you get

1. sinx = cosx
2. sinx = -cosx

Now we note that at the place where cosx = 0, sinx does not equal zero so we can freely divide by cosx and not worry about losing solutions.

From (1), tanx = 1. From (2), tanx = -1. As you said, pi/4 and 3pi/4 are the only two solutions

anonymous · Answer

@khoala4pham can 5pi/4 and 7pi/4 be the solutions also??

anonymous · Answer

Oh wow. Yeah. You're absolutely right. I was thinking of negative polar stuff. I apologize for that. Yes, both of those are solutions, too.

anonymous · Answer

@khoala4pham thankyou:)