If $2 \sin ^{2} \theta-\cos ^{2} \theta=2$, then find the value of $\theta$.

$5 \cos A=4 \sin A,$ then $\tan A=\ldots \ldots \cdots \cdots$

Write 'True' or 'False' and justify your answer.

The value of $\sin \theta+\cos \theta$ is always greater than $1$ .

Given that $\alpha+\beta=90^{\circ},$ show that

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

$\sin 70=\cos \theta,$ then $\theta=\ldots \ldots \ldots \ldots$