In $Fig.$ find $\tan P-\cot R .$
$1$
$5$
$0$
$12$
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 $B$
Evaluate the following:
$2 \tan ^{2} 45^{\circ}+\cos ^{2} 30^{\circ}-\sin ^{2} 60^{\circ}$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$(\sin A+\operatorname{cosec} A)^{2}+(\cos A+\sec A)^{2}=7+\tan ^{2} A+\cot ^{2} A$
If $\sin A =\frac{3}{4},$ calculate $\cos A$ and $\tan A$.
Evaluate $\frac{\tan 65^{\circ}}{\cot 25^{\circ}}$