Question

What are most of the people living in the village​

Answer 1

Explanation:

Prove that sin 20*sin40+sin60*sin80=3/16.

Answer:

Consider LHS

sin 20 × sin 40 × sin60 × sin80

Sin Values

sin 0° = √(0/4) = 0

sin 30° = √(1/4) = ½

sin 45° = √(2/4) = 1/√2

sin 60° = √3/4 = √3/2

sin 90° = √(4/4) = 1

LHS = sin60 [sin20 × sin40 × sin80]

LHS = √3/2[sin20 × sin(60 – 20) × sin(60 + 20)]

LHS = √3/2[sin 3(20)/4]

LHS = √3/2[sin 60/4]

LHS = √3/2[√3/2 × 4]

LHS = √3/2 × √3/8

LHS = 3/16

∴ LHS = RHS