Question

Cos10cos50cos60cos70=3/16 Can you prove it?

Answer 1

cos10°cos50°cos60°cos70°
=1/2(2cos10°cos50°)×1/2×cos70° [∵, cos60°=1/2]
=1/4{cos(10°+50°)+cos(10°-50°)}cos70°
=1/4(cos60°+cos40°)cos70°
=1/4cos60°cos70°+1/4cos40°cos70°
=1/4×1/2×cos70°+1/8(2cos40°cos70°)
=1/8cos70°+1/8{cos(40°+70°)+cos(40°-70°)}
=1/8cos70°+1/8cos110°+1/8cos30°
=1/8(cos70°+cos110°)+1/8×√3/2
=1/8{2cos(70°+110°)/2cos(70°-110°)/2}+√3/16
=1/8(2cos90°cos20°)+√3/16
=0+√3/16 [∵, cos90°=0]
=√3/16
If its cos10°cos30°cos50°cos70° then it will be 3/16 in rhs.

Answer 2

Answer:

follow the above procedure