If $\sin 3 A =\cos \left( A -26^{\circ}\right),$ where $3 A$ is an acute angle, find the value of $A= . . . . ^{\circ}$.
$29$
$32$
$20$
$25$
Given $15 \cot A =8,$ find $\sin A$ and $\sec A .$
$\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}}=$
Evaluate:
$\cos 48^{\circ}-\sin 42^{\circ}$
If $A , B$ and $C$ are interior angles of a triangle $ABC ,$ then show that
$\sin \left(\frac{B+C}{2}\right)=\cos \frac{A}{2}$
If $\tan 2 A=\cot \left(A-18^{\circ}\right),$ where $2 A$ is an acute angle, find the value of $A .$ (in $^{\circ}$)