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

Tried setting sin^2 x and -cos^2 x equal to zero, but that didn't work out...

Answer choices:
x = pi divided by four

x = pi divided by four, three pi divided by four, five pi divided by four, seven pi divided by four

x = seven pi divided by four, pi divided by three

x = seven pi divided by four, pi divided by six

tamtoan · Answer

you know that :

$$\sin^{2} x + \cos^{2} x = 1 $$
right? apply this to see what you get.

anonymous · Answer

I don't really understand what you mean.

tamtoan · Answer

with the formula there, you can eliminate either sin^2 (x) or cos^2(x) ...then solve it.

anonymous · Answer

sin^2 x = 0?

anonymous · Answer

not zero, 1?

tamtoan · Answer

let's add the 2 equations you have there and see what you get? ...sin^2(x) is not 1 ..it's twice of that is 1

anonymous · Answer

2 sin^2 x = 1?

tamtoan · Answer

yeah , then solve for x :)

anonymous · Answer

x = pi divided by four, three pi divided by four, five pi divided by four, seven pi divided by four ?

sirm3d · Answer

$$\Huge \color{blue} \checkmark $$

tamtoan · Answer

well, you have sin^2(x) = 1/2 ...take square root both side and you have sin(x) = $$1/\sqrt{2}$$  from here, you can use calculator to find out...i don't remember which one.