Answer:
3/16
Explanation:
Prove that sin 20 ×sin40 × sin60 × sin80 = 3/16.
We have to prove sin 20 × sin40 × sin60 × sin80 = 3/16.
Consider LHS
sin 20 × sin 40 × sin60 × sin80
Sin Values
In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function is used to find the unknown angle or sides of a right triangle.
We know the trigonometric values of sin function
Proof
Consider LHS
sin 20 × sin 40 × sin60 × sin80
= sin60 [sin20 × sin40 × sin80]
= √3/2[sin20 × sin(60 – 20) × sin(60 + 20)]
= √3/2[sin 3(20)/4]
= √3/2[sin 60/4]
= √3/2[√3/2 × 4]
= √3/2 × √3/8 = 3/16
∴ LHS = RHS
Hence proved