Math, asked by Marchii566, 3 months ago

Trigonometric formulas ​

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Answered by anupriya08735
0

I am not sure but this is right answer

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Answered by Anonymous
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Trigonometry Formulas

  • sin(−θ) = −sin θ
  • cos(−θ) = cos θ
  • tan(−θ) = −tan θ
  • cosec(−θ) = −cosecθ
  • sec(−θ) = sec θ
  • cot(−θ) = −cot θ

Product to Sum Formulas

  • sin x sin y = 1/2 [cos(x–y) − cos(x+y)]
  • cos x cos y = 1/2[cos(x–y) + cos(x+y)]
  • sin x cos y = 1/2[sin(x+y) + sin(x−y)]
  • cos x sin y = 1/2[sin(x+y) – sin(x−y)]

Sum to Product Formulas

  • sin x + sin y = 2 sin [(x+y)/2] cos [(x-y)/2]
  • sin x – sin y = 2 cos [(x+y)/2] sin [(x-y)/2]
  • cos x + cos y = 2 cos [(x+y)/2] cos [(x-y)/2]
  • cos x – cos y = -2 sin [(x+y)/2] sin [(x-y)/2]

Sum or Difference of angles

  • cos (A + B) = cos A cos B – sin A sin B
  • cos (A – B) = cos A cos B + sin A sin B
  • sin (A+B) = sin A cos B + cos A sin B
  • sin (A -B) = sin A cos B – cos A sin B
  • tan(A+B) = [(tan A + tan B)/(1 – tan A tan B)]
  • tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)]
  • cot(A+B) = [(cot A cot B − 1)/(cot B + cot A)]
  • cot(A-B) = [(cot A cot B + 1)/(cot B – cot A)]
  • cos(A+B) cos(A–B)=cos^2A–sin^2B=cos^2B–sin^2A
  • sin(A+B) sin(A–B) = sin^2A–sin^2B=cos^2B–cos^2A

Multiple and Submultiple angles

  • sin2A = 2sinA cosA = [2tan A /(1+tan²A)]
  • cos2A = cos²A–sin²A = 1–2sin²A = 2cos²A–1= [(1-tan²A)/(1+tan²A)]
  • tan 2A = (2 tan A)/(1-tan²A)

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