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Prove that, cos (60° +A) + cos(60°-A) – cosA = 0

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Prove that, cos (60° +A) + cos(60°-A) – cosA = 0

Solution:

cos (60° +A) + cos(60°-A) – cosA

= 2 cos $\left(\frac{60° + A + 60° – A}{2}\right)$ cos$\left(\frac{60° + A – 60° + A}{2}\right)$ – cosA

= 2 cos $\left(\frac{120°}{2}\right)$ cos $\frac{2A}{2}$ – cosA

= 2 cos 60° cos A – cosA

= 2 × $\frac{1}{2}$ ×cosA – cosA

= cosA – cosA

= 0

আরও দেখুন

  1. If psinα=q sin(120°+α)=r sin(240°+α) prove that pq+qr+rp=0
  2. Prove that, sinα +sin(120°+α) + sin(240°+α) = 0
  3. Prove That cos20° cos40° cos80° = 1/8
  4. Prove that sin10° +sin50° – sin70°= 0
  5. Prove that cos 80° – cos40° + $\sqrt{3}$ cos70° = 0

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