Prove that
sin50° - sin70° + sin10° = 0
To prove the equation sin50° - sin70° + sin10° = 0, we can use the trigonometric identity known as the sum-to-product formula.
The sum-to-product formula states that sin(A) - sin(B) = 2 * cos((A + B)/2) * sin((A - B)/2).
Applying this formula, we can rewrite the equation as:
sin50° - sin70° + sin10°
= 2 * cos((50° + 70°)/2) * sin((50° - 70°)/2) + sin10°
= 2 * cos(120°/2) * sin((-20°)/2) + sin10°
= 2 * cos(60°) * sin(-10°) + sin10°
Now, we need to simplify the expression further. We know that cos(60°) = 0.5 and sin(-10°) = -sin10°, so we can substitute these values:
2 * cos(60°) * sin(-10°) + sin10°
= 2 * 0.5 * (-sin10°) + sin10°
= -sin10° + sin10°
= 0
Hence, we have proven that sin50° - sin70° + sin10° = 0.