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\[-\left(\cos^2 \theta - \sin^2 \theta\right) = -1\]\[\implies -\cos(2\theta) = -1\]\[\implies \cos(2\theta) = 1\]Or use either of the two identities:\[\cos^2 \theta = 1 - \sin^2 \theta\]\[\sin^2 \theta = 1- \cos^2 \theta\]
So add \[\cos^2(\theta)\]
on both sides to use the identity that is being recalled
Now use the identity
which results into two equations
Just add those two equations to get \(2\sin^2 \theta = 0\).
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oh yeah that is pretty too
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.
3 of them actually
parth did one way at first
then he found another way off what i was doing