The general solution of the equation $\sqrt{6-5 \cos x+7 \sin ^2 x}-\cos x=0$ also satisfies the equation

The circumradius $R$ of an isosceles triangle $ABC$ is four times its inradius $r$. If $A = B$,then which of the following is true?

In $\triangle ABC$,if $\cos ^2 A + \cos ^2 B + \cos ^2 C = 1$,then $\triangle ABC$ is

In $\triangle ABC$,if $a=2, b=\sqrt{6}$,and $c=\sqrt{3}+1$,then $\sin^2 C - \sin^2 A =$

The value of $\theta$,satisfying both the equations $\cos \theta = \frac{1}{\sqrt{2}}$ and $\tan \theta = -1$ in the interval $[0, 2\pi]$,is

Statement $-1$: The number of common solutions of the trigonometric equations $2\sin^2\theta - \cos 2\theta = 0$ and $2\cos^2\theta - 3\sin\theta = 0$ in the interval $[0, 2\pi]$ is two.
Statement $-2$: The number of solutions of the equation $2\cos^2\theta - 3\sin\theta = 0$ in the interval $[0, \pi]$ is two.