Sum and differences of identities questions

Now Playing:Sum and difference identities – Example 1a

Simplify expressions
1. sin 24°cos 36° + cos 24°sin 36°
  
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2. $\frac{tan {2 \pi \over 5 } - tan {3 \pi \over 20}}{1 + \tan {2 \pi \over 5} \cdot \tan {3 \pi \over 20}}$
  
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Prove Identities
1. $\frac{\sin (A - B)}{\sin B} + \frac{\cos (A - B)}{\cos B} = \frac{\sin A}{\sin B \cos B}$
2. $\frac{1 + \tan A}{\tan (A + {\pi \over 4})} = 1 - \tan A$
Without using a calculator, evaluate:
1. sin 15°
  
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2. sec (-105°)
  
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3. tan ${19\pi \over 12}$
  
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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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