Sum Difference Double Half Angles Identities

 $\cos70^o\cos40^o-\sin70^o\sin40^o\$  is equivalent to

If  $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$   $and\ \angle A\ and\ \angle B$  are acute angles, what is the value of  $\cos\left(A-B\right)?$  

If $\cos A=\frac{1}{3}$  , then the positive value of  $\tan\ \frac{A}{2}$  ?

If $\tan A=\frac{2}{3}\ and\ \tan B=\frac{1}{2},$  what is the value of  $\tan\left(A+B\right)?$  

If $\sin A=\frac{4}{5},\tan B=\frac{5}{12},$  and A and B are first quadrant angles, what is the value of  $\sin\left(A+B\right)$  ?

 $\sin96^o\cos24^o+\cos96^o\sin24^o\$  is equivalent to

The expression $2\sin30^o\cos30^o$  has the same value as

If x is a positive acute angle and $\sin x=\frac{1}{2},$  what is  $\sin2x?$  

If $\cos\theta=\frac{1}{8},$  the positive value of  $\sin\ \frac{\theta}{2}$  is

If $\sin\theta=\frac{\sqrt{5}}{3}$  , then  $\cos2\theta$  equals