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Sin780 sin480+cos240cos300=1/2?
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Sin780 sin480+cos240cos300=1/2?
Explanation of sin780 sin480 cos240cos300=1/2


Trigonometric Identities Used:

  • sin(180° + θ) = -sinθ

  • sin(360° + θ) = sinθ

  • cosθ = -cos(180° + θ)

  • cosθ = cos(360° - θ)

  • cos(180° + θ) = -cosθ

  • cos(360° - θ) = cosθ

  • sinθcosθ = 1/2 * sin2θ



Solution:

sin780 = sin(720° + 60°) = sin60° = sin(360° + 60°) = sin60° = sin(180° + 60°) = -sin120°

sin480 = sin(360° + 120°) = sin120°

cos240 = cos(180° + 60°) = -cos60°

cos300 = cos(360° - 60°) = cos60°

sin780 sin480 cos240cos300 = -sin120° * sin120° * (-cos60°) * cos60°

= (1/2 * sin240°) * (1/2 * sin240°)

= 1/4 * sin^2(2 * 120°)

= 1/4 * sin^2(240°)

= 1/4 * sin^2(-120°)

= 1/4 * sin^2(240°)

= 1/4 * (1/2)^2

= 1/16

Therefore, sin780 sin480 cos240cos300 = 1/2 is false. The correct answer is 1/16.
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Sin780 sin480+cos240cos300=1/2?
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Sin780 sin480+cos240cos300=1/2?
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