The multiplication of sin 30° and sin 60° results in √3/2, representing the value of their product without any alteration.
To find the product of sin 30° and sin 60°, we can use the trigonometric identity for the sine of the sum of two angles. The identity states that sin(A + B) = sin(A)cos(B) + cos(A)sin(B).
Let's consider sin 30° and sin 60°:
sin 30° = 1/2
sin 60° = √3/2
Using the identity, we have:
sin (30° + 60°) = sin 30°cos 60° + cos 30°sin 60°
Now, we can substitute the values:
sin (30° + 60°) = (1/2)(√3/2) + (√3/2)(1/2)
Simplifying, we get:
sin (30° + 60°) = √3/4 + √3/4
Combining like terms, we have:
sin (30° + 60°) = 2√3/4
Now, let's simplify the expression:
sin (30° + 60°) = √3/2
Therefore, the product of sin 30° and sin 60° is √3/2
In summary, the product of sin 30° and sin 60° is equal to √3/2, which can be derived by using the trigonometric identity for the sine of the sum of two angles.
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