Using Sum and Difference Identities to Simplify an Expression (7.5.3)

Question 1

• Sum and difference identities can be useful in simplifying trigonometric expressions.

Answer 1

• Sum and difference identities can be useful in simplifying trigonometric expressions.

Question 2

• The sum and difference identities:
  
  • The sine of a sum of angles: sin (x1 + x2) = sinx1 + cosx2 + cosx1 + sinx2
  • The sine of a difference of angles: sin (x1 - x2) = sinx1cosx2 - cosx1sinx2
  • The cosine of a sum of angles: cos (x1 + x2) = cosx1cosx2 - sinx1sinx2
  • The cosine of a difference of angles: cos (x1 + x2) = cosx1cosx2 + sinx1sinx2
  • The tangent of a sum of angles: tan(x1 + x2) = (tanx1 + tanx2)/1-tanx1*tanx2
  • The tangent of a difference of angles: tan(x1 + x2) = (tanx1 - tanx2)/1+tanx1*tanx2

x = theta

Answer 2

• The sum and difference identities:
  
  • The sine of a sum of angles: sin (x1 + x2) = sinx1 + cosx2 + cosx1 + sinx2
  • The sine of a difference of angles: sin (x1 - x2) = sinx1cosx2 - cosx1sinx2
  • The cosine of a sum of angles: cos (x1 + x2) = cosx1cosx2 - sinx1sinx2
  • The cosine of a difference of angles: cos (x1 + x2) = cosx1cosx2 + sinx1sinx2
  • The tangent of a sum of angles: tan(x1 + x2) = (tanx1 + tanx2)/1-tanx1*tanx2
  • The tangent of a difference of angles: tan(x1 + x2) = (tanx1 - tanx2)/1+tanx1*tanx2

x = theta