Tangent Addition Formula To prove the tangent addition and subtraction formulas, we will use the identity sin x tan x = COS x Fill in the blanks using our sine addition and cosine addition formulas: 9) tan ( x + y) = = sin(xty) Sinx cosy + cosx sing cos(x+y) Cosx Cosy - Sink siny Now divide each term in the numerator and denominator by cos x . cos y, so write your numerator on the numerator section, and your denominator as the numerator part of the entire denominator Sinx Cosy, Cosa Siny 10) cosx cosy 'cosx.cosy sinx Cosy CORsiny cosx.cosy cosx.cosy Simplify each fraction. 11) 12) Now using your trig identity, tan x = to change back to tangent to finish the formula. cosx CosX