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Find the value of sin20 × sin30 × sin40 × sin80.


Please I need answers...​

User Remko Popma
by
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1 Answer

4 votes
4 votes

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

Find the value of sin20 × sin30 × sin40 × sin80. Please I need answers...​-example-1
User Or Choban
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