Question

Can someone help me with a trig formula problem?

Answer 1

\[\cos^2\theta + 2\sin \theta \cos \theta-\sin^2\theta=0\] is the original

\[\cos(2\theta) + \sin (2\theta) = 0\] then I use formulas to get to this

Answer 2

i would not use the formula too confusing

Answer 3

solve
\[\sin(x)=-\cos(x)\] in your head, the replace \(x\) by \(2\theta\)

Answer 4

one is the negative of the other when \(x=\frac{3\pi}{4}\) or \(\frac{7\pi}{4}\) at those points one is \(\frac{\sqrt2}{2}\) and the other is \(-\frac{\sqrt2}{2}\)

Answer 5

Does it matter if we make the sin or cos negative

Answer 6

no

Answer 7

one is the negative of the other at those to places