If $\tan \alpha = \frac{1}{7}$ and $\tan \beta = \frac{1}{3}$,then $\cos 2\alpha = $

Let $f(x) = \sin^2 x + \cos^4 x + 2$ and $g(x) = \cos(\cos x) + \cos(\sin x)$. If the periods of $f(x)$ and $g(x)$ are $T_1$ and $T_2$ respectively,then:

If $\tan^2 \alpha \tan^2 \beta + \tan^2 \beta \tan^2 \gamma + \tan^2 \gamma \tan^2 \alpha + 2 \tan^2 \alpha \tan^2 \beta \tan^2 \gamma = 1$,then the value of $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$ is

If $\cos \theta = \frac{1}{2}\left( x + \frac{1}{x} \right)$,then $\frac{1}{2}\left( x^2 + \frac{1}{x^2} \right) = $

Let $E = \left( {1 - \frac{{\cos 61^\circ}}{{\cos 1^\circ}}} \right) \left( {1 - \frac{{\cos 62^\circ}}{{\cos 2^\circ}}} \right) \dots \left( {1 - \frac{{\cos 119^\circ}}{{\cos 59^\circ}}} \right)$,then $E$ is equal to:

Let $A = \{ \theta : 2\cos^2 \theta + \sin \theta \le 2 \}$ and $B = \{ \theta : \frac{\pi}{2} \le \theta \le \frac{3\pi}{2} \}$,then $A \cap B$ is