Given both $$\theta $$ and $$\phi $$ are acute angles and $$\sin \,\theta = {1 \over 2},\,$$ $$\cos \,\phi = {1 \over 3},$$ then the value of $$\theta + \phi $$ belongs to

The number of integral values of $$k$$ for which the equation $$7\cos x + 5\sin x = 2k + 1$$ has a solution is

The maximum value of $$\left( {\cos {\alpha _1}} \right).\left( {\cos {\alpha _2}} \right).....\left( {\cos {\alpha _n}} \right),$$ under the restrictions
$$0 \le {\alpha _1},{\alpha _2},....,{\alpha _n} \le {\pi \over 2}$$ vand $$\left( {\cot {\alpha _1}} \right).\left( {\cot {\alpha _2}} \right)....\left( {\cot {\alpha _n}} \right) = 1$$ is

If $$\alpha + \beta = \pi /2$$ and $$\beta + \gamma = \alpha ,$$ then $$\tan \,\alpha \,$$ equals