$\cos 35^{\circ} = \ldots \ldots \ldots$

In a right triangle $ABC$,right-angled at $B$. If $\tan A = 1$,then verify that $2 \sin A \cos A = 1$.

Write 'True' or 'False' and justify your answer.
The value of the expression $(\sin 80^{\circ} - \cos 80^{\circ})$ is negative.

Write 'True' or 'False' and justify your answer.
The value of $2 \sin \theta$ can be $(a + \frac{1}{a}),$ where $a$ is a positive number,and $a \neq 1$.

Write 'True' or 'False' and justify your answer.
$\cos \theta = \frac{a^{2} + b^{2}}{2ab}$,where $a$ and $b$ are two distinct numbers such that $ab > 0$.

If $3 \cot \theta = 4$,then $\frac{1 - \tan^2 \theta}{1 + \tan^2 \theta} = \dots$