Could any kind souls help me with these questions? I am stuck!

1)Prove the identity: cos(a+b) cos(a-b) = cos^2a -sin^2b

for this, i am stuck at LHS = cos^2a cos^2b - sin^2a sin^2b .

2)Prove the identity tanA tan(A-60) + tanA tan(A+60) + tan(A-60) tan(A+60) = -3,

For this,im stuck with LHS = -3tan^2A . Please correct me if this is already wrong cause i assumed A to be 180 degrees.

3)If A and B are the principal values of arccos(3/sqrt10) and arcsin(1/sqrt5) respectively,show that A+B = pi/4(I have no idea how to start this,i've never seen this question before!)

4)Prove that if A+B+C = 180 degrees(sum of angles in a triangle),

cotAcotB + cotBcotC + cotCcotA =1 holds true.

(for this, i've tried to use 1/tanAtanB... and also converting it to cosA/sinA... but both of these methods got me into infinite loops and some nice symmetry too. Haha!)

All help is greatly appreciated!