If $A+B=\frac{\pi}{2}$,then the maximum value of $\cos A \cdot \cos B$ is

Assertion $(A)$: If $\alpha=12^{\circ}, \beta=15^{\circ}, \gamma=18^{\circ}$,then $\tan 2 \alpha \tan 2 \beta+\tan 2 \beta \tan 2 \gamma+\tan 2 \gamma \tan 2 \alpha=1$.
Reason $(R)$: In $\triangle ABC$,$\tan \frac{A}{2} \tan \frac{B}{2}+\tan \frac{B}{2} \tan \frac{C}{2}+\tan \frac{C}{2} \tan \frac{A}{2}=1$.
Which of the following is true?

For all values of $\theta$,the values of $3-\cos \theta+\cos \left(\theta+\frac{\pi}{3}\right)$ lie in the interval :

Let $y=4 \sin^2 \theta - \cos 2 \theta$. If $l$ and $m$ are the minimum and maximum values of $y$ respectively,then

If $A + B + C = 180^o$,then $\sum \tan \frac{A}{2} \tan \frac{B}{2} = $

If the equation $\cos^4 \theta + \sin^4 \theta + \lambda = 0$ has real solutions for $\theta$,then $\lambda$ lies in the interval