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Alex17521 [72]
2 years ago
7

if a and b are acute angles such that sinA=4/5 and cosB=12/13, calculate, without using tables: sin(a-b)

Mathematics
1 answer:
kolbaska11 [484]2 years ago
7 0
\sin \alpha = \frac{4}{5} \\ \cos \alpha  =  \sqrt{1-\sin^2 \alpha }= \sqrt{1- \frac{16}{25} }   = \sqrt{ \frac{9}{25} }= \frac{3}{5} \\    \\ \cos \beta = \frac{12}{13}  \\  \sin \beta  =  \sqrt{1-\cos^2  \beta }= \sqrt{1- \frac{144}{169} }   = \sqrt{ \frac{25}{169} }= \frac{5}{13}


\\  \\ \sin (\alpha- \beta ) =\sin \alpha \cos \beta -\cos \alpha \sin \beta = \frac{4}{5}\times \frac{12}{13}-   \frac{3}{5}\times \frac{5}{13} =  \frac{48}{65}- \frac{15}{65}=  \frac{33}{65}

Answer:
sin(α-β) = 33/65
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