Questions in trigonometry

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If $x=a{{\cos }^{3}}\theta ,y=b{{\sin }^{3}}\theta ,$then
If $\cot \,\theta +\tan \theta =m$and $\sec \theta -\cos \theta =n,$then which of the following is correct
${{\sin }^{6}}\theta +{{\cos }^{6}}\theta +3{{\sin }^{2}}\theta {{\cos }^{2}}\theta =$
The value of $2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1$ is
If $\sin x+{{\sin }^{2}}x=1$, then the value of ${{\cos }^{12}}x+3{{\cos }^{10}}x+3{{\cos }^{8}}x+{{\cos }^{6}}x-2$ is equal to
If $\cos x+{{\cos }^{2}}x=1,$then the value of ${{\sin }^{2}}x+{{\sin }^{4}}x$ is
If $\sin x+{{\sin }^{2}}x=1,$then ${{\cos }^{8}}x+2{{\cos }^{6}}x+{{\cos }^{4}}x=$
If $x{{\sin }^{3}}\alpha +y{{\cos }^{3}}\alpha =\sin \alpha \cos \alpha $ and $x\sin \alpha -y\cos \alpha =0,$ then ${{x}^{2}}+{{y}^{2}}=$
If $(1+\sin A)(1+\sin B)(1+\sin C)=(1-\sin A)(1-\sin B)(1-\sin C),$then each side is equal to
If $(\sec \alpha +\tan \alpha )(\sec \beta +\tan \beta )(\sec \gamma +\tan \gamma )=\tan \alpha \tan \beta \tan \gamma $, then $(\sec \alpha -\tan \alpha )(\sec \beta -\tan \beta )$ then $(\sec \gamma -\tan \gamma )=$

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