## kassandratb 2 years ago find all solutions of sin^2theta=cos^2theta

1. mathstudent55

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2. kassandratb

what do i do one i've done this

3. JamesJ

Well, remember that cos(2x) = cos^2 x - sin^2 x So if cos^2 x = sin^2 x then cos^2 x - sin^2 x = 0 or cos(2x) = 0 Can you take it from here?

4. kassandratb

when I do this : cos^2x-sin^2x=0 cos(2x)=0 cosx=0 x=pi, 2pi, +2k ?

5. kassandratb

JamesJ i feel like i did this wrong

6. mathstudent55

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7. Mertsj

You need to make a substitution. Replace sin^2 theta with 1 - cos^2 theta or replace cos^2 theta with 1-sin^2 theta.

8. JamesJ

If cos(2x) = 0 then 2x = pi/2 + k.pi, for any integer k. Hence x = pi/4 + k.pi/2, for any integer k.

9. JamesJ

You can see those solutions on this graph as well.

10. Mertsj

$\sin^2\theta =1-\sin ^2\theta$ $2\sin ^2\theta =1$ $\sin^2\theta =\frac{1}{2}$ $\sin \theta = \pm \frac{\sqrt{2}}{2}$ $\theta = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4} + 2\pi n$

11. kassandratb

Thank you all it's starting to make a lot more since to me now so I just gotta know my identities?

12. Mertsj

Yes. That is key.