Trigo formula

Trigo formula

1. t = tan A/2

   • tan A = 2t / (1-t^2)
   • cos A = (1 - t^2) / (1 + t^2)
   • sin A = 2t / (1 + t^2)

2. Product formula

   • sin A + sin B = 2 sin [(A+B) /2] cos [(A-B) /2]
   • sin A - sin B = 2 cos [(A+B) /2] sin [(A-B) /2]
   • cos A + cos B = 2 cos [(A+B) /2] cos [(A-B) /2]
   • cos A - cosB = - 2 sin [(A+B) /2] sin [(A-B) /2]

3. Equalities

   • sin^2 x+ cos^2 =1
   • 1 + tan^2 x = sec^2 x
   • 1+cot^2 x = csc^ x

4. 和角公式

   • sin (A+B) = sin A cos B + cos A sin B
   • cos (A+B) = cos A cos B - sin A sin B
   • tan (A+B) = (tan A+ tan B) / (1 - tanA tanB)
   • sin (A-B) = sin A cos B - cos A sin B
   • cos (A-B) = cos A cos B + sin A sin B
   • tan (A-B) = (tan A - tan B) / (1 + tanA tanB)