\[\sqrt{3}\,\text{cosec}\,{{20}^{o}}-\sec \,{{20}^{o}}=\] [IIT 1988]

\[1+\cos \,{{56}^{o}}+\cos \,{{58}^{o}}-\cos {{66}^{o}}=\] [IIT 1964]

If \[x=\sin {{130}^{o}}\,\cos {{80}^{o}},\,\,y=\sin \,{{80}^{o}}\,\cos \,{{130}^{o}},\,\,z=1+xy,\]which one of the following is true [AMU 1999]

If \[\sin \alpha =1/\sqrt{5}\]and \[\sin \beta =3/5\],then \[\beta -\alpha \]lies in the interval [Roorkee Qualifying 1998]

If \[2\sec 2\alpha =\tan \beta +\cot \beta ,\]then one of the values of \[\alpha +\beta \]is [Karnataka CET 2000]

\[\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{6}\] is equal to [IIT 1966, 1975]

If \[\tan \,(A+B)=p,\,\,\tan \,(A-B)=q,\] then the value of \[\tan \,2A\] in terms of p and q is [MP PET 1995, 2002]

\[2\,{{\sin }^{2}}\beta +4\,\,\cos \,(\alpha +\beta )\,\,\sin \,\alpha \,\sin \,\beta +\cos \,2\,(\alpha +\beta )=\] [MNR 1993; IIT 1977]

The value of \[\sin \theta +\cos \theta \] will be greatest when [MNR 1977, 1983; RPET 1995]

If \[f(x)={{\cos }^{2}}x+{{\sec }^{2}}x,\] then[MNR 1986]

If \[A+B+C=\pi \] and \[\cos A=\cos B\,\cos C,\] then \[\tan B\,\,\tan C\] is equal to [AMU 2001]

If \[A+C=B,\] then \[\tan A\,\tan B\,\tan C=\] [EAMCET 1986]

If \[\left| \cos \,\theta \,\left\{ \sin \theta +\sqrt{{{\sin }^{2}}\theta +{{\sin }^{2}}\alpha } \right\}\, \right|\,\le k,\] then the value of k is

If \[\sin x+\text{cosec}\,x=2,\] then \[4\sin A\,\,\sin B\,\,\sin C\] is equal to [UPSEAT 2002]

If \[\sin \theta +\text{cosec}\theta =2,\] the value of \[{{\sin }^{10}}\theta +\text{cose}{{\text{c}}^{10}}\theta \] is [MP PET 2004]