Question
Download Solution PDFIf sin A = \(\frac{4}{5}\) and sin B = \(\frac{15}{17}\), what is the value of sin (A - B)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
sin A = \(\frac{4}{5}\) and sin B = \(\frac{15}{17}\)
Concept used:
sin (A - B) = sinAcosB - cosAsinB
Calculation:
sin A = \(\frac{4}{5}\)
So, cos A = \(\frac{3}{5}\)
Again,
sin B = \(\frac{15}{17}\)
So, cos B = \(\frac{8}{17}\)
Now,
sin (A - B) = sinAcosB - cosAsinB
⇒ \(\frac{4}{5}\) × \(\frac{8}{17}\) - \(\frac{3}{5}\) × \(\frac{15}{17}\)
⇒ \(\frac{32}{85}\) - \(\frac{45}{85}\)
⇒ - \(\frac{13}{85}\)
∴ The required answer is \(-\frac{13}{85}\).
Last updated on Jul 8, 2025
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