Sum and difference identities

Lessons

Download the Trigonometry identities chart here

Formulas:

$\sin (A + B)$

$\sin (A - B)$

$\cos (A + B)$

$\cos (A - B)$

$\tan (A + B)$

$\tan (A - B)$

• 1.
  Simplify expressions

  
  
  a)

  sin 24°cos 36° + cos 24°sin 36°
  
  
  
  b)

  $\frac{tan {2 \pi \over 5 } - tan {3 \pi \over 20}}{1 + \tan {2 \pi \over 5} \cdot \tan {3 \pi \over 20}}$
  
  
  

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• 2.
  Prove Identities
  a)

  $\frac{\sin (A - B)}{\sin B} + \frac{\cos (A - B)}{\cos B} = \frac{\sin A}{\sin B \cos B}$
  
  
  
  b)

  $\frac{1 + \tan A}{\tan (A + {\pi \over 4})} = 1 - \tan A$
  
  
  

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• 3.
  Without using a calculator, evaluate:
  a)

  sin 15°
  
  
  b)

  sec (-105°)
  
  
  c)

  $tan {19\pi \over 12}$
  
  
  

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• 4.
  Given $\sin A = -{4 \over5}$ and $\cos B = {12 \over 13} ,$
  where $\pi \leq A \leq {3 \pi \over 2}$ and ${3 \pi \over 2} \leq B \leq 2\pi ,$
  find the exact value of $\cos (A + B)$

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