$\left(1+\tan ^{2} \theta\right)\left(1-\cos ^{2} \theta\right)=\ldots \ldots \ldots$

$\operatorname{cosec} \theta=\frac{2}{\sqrt{3}},$ તો $\theta=\ldots \ldots \ldots \ldots$

$\sin x=\sin 60 \cdot \cos 30-\cos 60 \cdot \sin 30,$ તો $x=\ldots \ldots \ldots \ldots$

જો $\alpha+\beta=90^{\circ}$ હોય, તો સાબિત કરો કે

$\sqrt{\cos \alpha \operatorname{cosec} \beta-\cos \alpha \sin \beta}=\sin \alpha$

$\sin \theta=\frac{1}{2},$ તો $\theta=\ldots \ldots \ldots \ldots$