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The value of sin 24 sin 48 sin96 sin192 is?
Most Upvoted Answer
The value of sin 24 sin 48 sin96 sin192 is?

Solution:

Given:
sin 24° * sin 48° * sin 96° * sin 192°

Using the formula:
sin (180 - θ) = sin θ

Breaking down the expression:
sin 24° * sin 48° * sin 96° * sin 192°
= sin 24° * sin 48° * sin (180 - 96)° * sin (180 - 48)°
= sin 24° * sin 48° * sin 84° * sin 132°

Using the formula:
sin (180 - θ) = sin θ

Further simplifying the expression:
= sin 24° * sin 48° * sin 84° * sin 132°
= sin 24° * sin 48° * sin (180 - 84)° * sin (180 - 132)°
= sin 24° * sin 48° * sin 96° * sin 48°

Combining the terms:
sin 24° * sin 48° * sin 96° * sin 192° = sin 24° * sin 48° * sin 96° * sin 48°

Using the formula:
sin θ * sin φ = 1/2 * [cos (θ - φ) - cos (θ + φ)]

Applying the formula:
sin 24° * sin 48° * sin 96° * sin 48°
= 1/2 * [cos (24 - 48)° - cos (24 + 48)°]
= 1/2 * [cos (-24)° - cos 72°]
= 1/2 * [cos 24° - cos 72°]

Result:
Therefore, the value of sin 24° * sin 48° * sin 96° * sin 192° is 1/2 * [cos 24° - cos 72°].
Community Answer
The value of sin 24 sin 48 sin96 sin192 is?
Sin(24)×sin(48)×sin(96)×sin(192)
= -0.0625
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