$\frac{1}{\cos ^{2} \theta}-\frac{1}{\cot ^{2} \theta} = \dots$

$\tan (65^\circ - \theta) - \cot (25^\circ + \theta) - \sec (55^\circ - \theta) + \operatorname{cosec}(35^\circ + \theta) = \ldots \ldots \ldots \ldots$ (where,$0 < \theta < 25^\circ$)

Write 'True' or 'False' and justify your answer.
The value of the expression $(\cos^{2} 23^{\circ} - \sin^{2} 67^{\circ})$ is positive.

$0 < \theta < 90$ and $\sec \theta = \operatorname{cosec} 60^\circ$,then the value of $2 \cos^2 \theta - 1$ is ........

$(1-\cos \theta)(1+\cos \theta) = \dots$

$\sin \theta \cdot \cos (90^\circ - \theta) = \ldots \ldots \ldots$