Sum and difference identities practice

Find the exact value of the expression.
$$\sin\left(\frac{5\pi}{12}\right)\cos\left(\frac{\pi}{4}\right)-\cos\left(\frac{5\pi}{12}\right)\sin\left(\frac{\pi}{4}\right)$$  

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

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

If A and B are first quadrant angles with sinA=15/17 and cosB=4/5, find cos(A - B).

Using the sum and difference formulas, condense into a single trig function:  $$\cos\left(46°\right)\cos\left(14°\right)+\sin\left(46°\right)\sin\left(14°\right)$$  

Find the exact value of the expression.

cos(20)cos(40) - sin(20)sin(40)

Which of the following is equivalent to $$\sin\left(\alpha+\beta\right)$$  ?

Which of the following is equivalent to $$\tan\left(\alpha+\beta\right)$$  ?

In the Pythagorean identity, $$\sin^2⁡θ+\cos^2⁡θ$$   is equal to what?

Complete the following sum or difference identity: $$\cos\ A\cos\ B\ -\ \sin\ A\sin\ B=$$ ​ (a)