Question

Prove that cos 20° cos 40° cos 60° cos 80° = 1/16.

Answer 1

Answer:

Answer: It's proved that cos 20° · cos40° · cos60°. cos80° = 1/16

Explanation: We know that, cos60° = 1/2. ...

2 cosa cosb= cos(a+b) + cos(a-b) Thus, 2 cos 20°cos80° = cos(20+80)° + cos(20-80)° Substituting back to (1) we get, ...

2cosa cosb = cos(a+b) + cos(a-b) Thus, 2 cos40° cos100° = cos(40+100)° + cos(40-100)°

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Solution :

We have,

cos 20° cos 40° cos 60° cos 80°

➡ ½ cos60° cos40°(2 cos80° cos20°)

➡ ½ × ½ cos40°•{cos(80°+20°) + cos(80°-20°)}

➡ ¼ cos40°(cos100° + cos60°)

➡ ¼ cos40°(cos100° + ½)

➡ ⅛ (2cos100° cos40°) + ⅛ cos40°

➡ ⅛ [cos(100° + 40°) + cos (100° - 40°)] + ⅛ cos40°

➡ ⅛ (cos140° + cos60°) + ⅛ cos40°

➡ ⅛ cos 140° + 1/16 + ⅛ cos 40°

➡ ⅛ cos (180° - 40°) + 1/16 + ⅛ cos 40°

➡ -⅛ cos40° + 1/16 + ⅛ cos40°

➡ 1/16 = RHS.

Hence :

Proved.