If A lies in third quadrant, and $20 \tan A = 21$, then the value of $\frac{5 \sin A - 2 \cos A}{4 \cos A - \frac{5}{7} \sin A}$.
Answer & explanation
Correct answer: option 2
20 tanA = 21
tanA = \(\frac{21}{20}\)
{ we know, tanA = \(\frac{P}{B}\) }
Now,
\(\frac{5sinA - 2cosA }{4 cosA - 5/7sinA}\)
= \(\frac{5 × P/H - 2 × B/H }{4 × B/H - 5/7 × P/H}\)
= \(\frac{5 × P - 2 × B }{4 × B - 5/7 × P}\)
= \(\frac{5 × 21 - 2 × 20 }{4 × 20 - 5/7 × 21}\)
= \(\frac{105 - 40 }{80 - 15}\)
= \(\frac{65 }{65}\)
= 1