Find the value of 4sin 20-sin 40-sin 60-sin 80-

We know that sin A·sin (60^∘ A)sin (60^∘+A)=1/4sin 3A Using the above formula sin 20^∘·sin 40^∘·sin 80^∘ =sin 20^∘·sin (60^∘ 20^∘)·sin (60^∘+20^∘) =1/4sin 60^ ...

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Standard X

Mathematics

Trigonometric Ratios of Complementary Angles

Find the valu...

Question

Find the value of $4 sin 20^{\circ} \cdot sin 40^{\circ} \cdot sin 60^{\circ} \cdot sin 80^{\circ}$

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Solution

We know that $sin A \cdot sin (60^{\circ} - A) sin (60^{\circ} + A) = \frac{1}{4} sin 3 A$
Using the above formula
$sin 20^{\circ} \cdot sin 40^{\circ} \cdot sin 80^{\circ} = sin 20^{\circ} \cdot sin (60^{\circ} - 20^{\circ}) \cdot sin (60^{\circ} + 20^{\circ}) = \frac{1}{4} sin 60^{\circ}$

$∴ 4 sin 20^{\circ} \cdot sin 40^{\circ} \cdot sin 60^{\circ} \cdot sin 80^{\circ} = 4 \cdot \frac{1}{4} \cdot {sin}^{2} 60^{\circ} = \frac{3}{4}$

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Similar questions

Q. Find:

sin 20 \times sin 40 \times sin 60 \times sin 80

sin 20^{\circ} sin 40^{\circ} sin 60^{\circ} sin 80^{\circ} = \frac{k}{16}

. Find the value of

k

$s i n 20^{\circ} s i n 40^{\circ} s i n 60^{\circ} s i n 80^{\circ}$ =

evaluate:

sin 20 \cdot sin 40 \cdot sin 60. s i n 80

Q. Sin20°sin40° sin60°. Sin80° =3/10

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Find the value of 4sin20∘⋅sin40∘⋅sin60∘⋅sin80∘

We know that sinA⋅sin(60∘−A)sin(60∘+A)=14sin3A Using the above formula sin20∘⋅sin40∘⋅sin80∘=sin20∘⋅sin(60∘−20∘)⋅sin(60∘+20∘)=14sin60∘ ∴4sin20∘⋅sin40∘⋅sin60∘⋅sin80∘=4⋅14⋅sin260∘=34

Find the value of $4 sin 20^{\circ} \cdot sin 40^{\circ} \cdot sin 60^{\circ} \cdot sin 80^{\circ}$