Evaluate $\frac{\tan 65^{\circ}}{\cot 25^{\circ}}$
$0$
$2$
$5$
$1$
If $\sin ( A - B )=\frac{1}{2}, \cos ( A + B )=\frac{1}{2}, 0^{\circ} < A + B \leq 90^{\circ}, A > B ,$ find $A$ and $B$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$(\sin A+\operatorname{cosec} A)^{2}+(\cos A+\sec A)^{2}=7+\tan ^{2} A+\cot ^{2} A$
$(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)=..........$
$\sin 2 A=2 \sin A$ is true when $A=$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\frac{\tan \theta}{1-\cot \theta}+\frac{\cot \theta}{1-\tan \theta}=1+\sec \theta \operatorname{cosec} \theta$