Revision/Test(Compound Angle)

1) Prove: tan 11A tan 7A tan 4A = tan 11A - tan 7A - tan 4A.

2) If sin(x+ y)= 4/5, cos(x - y)= 12/13, Find tan 2x.

3) Show: cos 2x cos 2y + sin²(x - y)- sin²(x + y)= cos(2x + 2y).

4) Prove: 4 sin(π/3  - x) sin(π/3 + x)= 3 - 4 sin²x.

5) Show that tan 75= {(√3+ 1)/(√3 - 1)}= 2+ √3. Hence show that tan 75 - cot 75 = 4 sin60.