Question
Download Solution PDFIf 8 tan A = 5, what is the value of \(\frac{8 \sin A-7 \cos A}{8 \sin A+11 \cos A} \)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
8 tan A = 5
Formula used:
\(\tan A = \dfrac{\sin A}{\cos A}\)
Calculation:
Given:
⇒ \(\dfrac{\sin A}{\cos A} = \dfrac{5}{8}\)
Let \(\sin A = 5k\) and \(\cos A = 8k\)
Now, substitute in the given expression:
⇒ \(\dfrac{8(5k) - 7(8k)}{8(5k) + 11(8k)}\)
⇒ \(\dfrac{40k - 56k}{40k + 88k}\)
⇒ \(\dfrac{-16k}{128k}\)
⇒ \(-\dfrac{1}{8}\)
∴ The correct answer is \(\frac{-1}{8}\).
Last updated on Jun 3, 2025
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