[Math] Trigonometric equation $ 2\cos^2\theta -\cos\theta-1 = \sin^2θ $

trigonometry

I have the following equation, and I have been stumped on it for a long time now, I was wondering if I could get some hints in attempting to solve it.

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

Solved!

Use the hyperbolic function (Thanks svenkatr):

$$ \cos^2\theta – \sin^2\theta = 1 $$

Best Answer

Write $\sin^2 \theta = 1- \cos^2 \theta$, simplify to get a quadratic equation in $\cos \theta$ and solve the equation.

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