amydh one year ago sin^2 theta - cos^2 theta = -1

1. ParthKohli

$-\left(\cos^2 \theta - \sin^2 \theta\right) = -1$$\implies -\cos(2\theta) = -1$$\implies \cos(2\theta) = 1$Or use either of the two identities:$\cos^2 \theta = 1 - \sin^2 \theta$$\sin^2 \theta = 1- \cos^2 \theta$

2. myininaya

or ... ANOTHER WAY! $\sin^2(\theta)-\cos^2(\theta)=-1$ Recall $\sin^2(\theta)+\cos^2(\theta)=1$ So add $\cos^2(\theta)$ on both sides to use the identity that is being recalled $\sin^2(\theta)+\cos^2(\theta)-\cos^2(\theta)=-1+\cos^2(\theta)$ Now use the identity $1-\cos^2(\theta)=-1+\cos^2(\theta)$ $2=2\cos^2(\theta)$ $1=\cos^2(\theta)$ which results into two equations

3. ParthKohli

Just add those two equations to get $$2\sin^2 \theta = 0$$.

4. myininaya

oh yeah that is pretty too

5. mathslover

This problem can be done in several ways. I was going to write some of them here, but I guess, they will all be actually similar to each other. But @myininaya and @ParthKohli have done well to find 2 of them.

6. myininaya

3 of them actually

7. myininaya

parth did one way at first then he found another way off what i was doing

8. ParthKohli

why are you typing like satellite does