Questions in trigonometry

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$\frac{\sin (B+A)+\cos (B-A)}{\sin (B-A)+\cos (B+A)}=$
If $\frac{\sin (x+y)}{\sin (x-y)}=\frac{a+b}{a-b},$then $\frac{\tan x}{\tan y}$ is equal to
If $\sin A+\sin 2A=x$ and $\cos A+\cos 2A=y,$ then $({{x}^{2}}+{{y}^{2}})({{x}^{2}}+{{y}^{2}}-3)=$
The expression $\frac{\cos 6x+6\cos 4x+15\cos 2x+10}{\cos 5x+5\cos 3x+10\cos x}$ is equal to
$\cos \alpha .\sin (\beta -\gamma )+\cos \beta .\sin (\gamma -\alpha )+\cos \gamma .\sin (\alpha -\beta )=$
$\sin (\beta +\gamma -\alpha )+\sin (\gamma +\alpha -\beta )+\sin (\alpha +\beta -\gamma )-\sin (\alpha +\beta +\gamma )=$
If $m\tan (\theta -30{}^\circ )=n\tan (\theta +120{}^\circ ),$ then $\frac{m+n}{m-n}=$
$2\cos x-\cos 3x-\cos 5x=$
$1+\cos 2x+\cos 4x+\cos 6x=$
If $\frac{\sin A-\sin C}{\cos C-\cos A}=\cot B,$ then A,B,C are in

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