Question

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Answer 1

You should find the usual expansion for the cosine of a difference. That would be an excellent place to start.

Also, if both a and b are in the 1st Quadrant, with b < a (How do I know that?), then a - b is also in the 1st quadrant. (Why do I care?)

Answer 2

\(\bf cos(a) = \cfrac{5}{13}\qquad \qquad cos(b) = \cfrac{3}{5}\\
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cos(a) = \cfrac{5}{13}\implies \cfrac{adjacent}{hypotenuse}\implies \cfrac{a}{c}\\
c^2= a^2 + b^2 \implies \sqrt{c^2-a^2}=b\qquad \qquad sin(a) = \cfrac{b}{c}\\
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cos(b) = \cfrac{3}{5}\implies \cfrac{adjacent}{hypotenuse}\implies \cfrac{a}{c}\\
c^2= a^2 + b^2 \implies \sqrt{c^2-a^2}=b\qquad \qquad sin(b) = \cfrac{b}{c}\)

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