Please help~

1)
cos(20)*cos(40)*cos(80)=1/2*[cos(20+40)+cos(20-40)]*cos(80)
=1/2*[cos(60)+cos(-20)]*cos(80)
=1/2*[1/2+cos(20)]*cos(80)
=1/4*cos(8)+1/2*cos(20)*cos(80)
=1/4*cos(80)+1/4*[cos(20+80)+cos(20-80)]
=1/4*cos(80)+1/4*[cos(100)+cos(-60)]
=1/4*cos(80)+1/4*cos(100)+1/4*cos(60)
=1/4*cos(80)+1/4*cos(180-80)+1/8
=1/4*cos(80)-1/4*cos(80)+1/8
=1/8 is final answer

2)
Proof : 2 sin(A + B) sinC = 1 - cos 2C
A+B+C =180
A+B = 180 - C
LHS = 2 sin(A+B) sinC
= 2 sin(180 - C) sinC
= 2[sin 180 cosC - cos 180 sinC] sinC
= 2[sinC] sinC
= 2(sinC)^2
RHS = 1 - cos 2C
= 1 - [1-2(sinC)^2]
= 2(sinC)^2 = LHS
so 2 sin(A + B) sinC = 1 - cos 2C

I hope this can help your understanding. =)