Question

sin^2 theta - cos^2 theta = -1

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

oh yeah that is pretty too

Answer 5

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.

Answer 6

3 of them actually

Answer 7

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

Answer 8

why are you typing
like satellite does