Question

if 5 tan A = 4. show 5sinA-3cosA/5sinA+3cosA=1/7​

Answer 1

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Answer 2

Answer:

Given,

$\sf \: 5 \: tan \: A = 4 \\\\\sf \: tan \: A = \frac{4}{5}$

Now,

$\sf \: \frac{(5 \: sin \: A– 3 \: cos \: A)}{(5 \: sin \: A + 3 \: cos \: A)}$

• Dividing the numerator and denominator by cos A,

$\sf \frac{(5 \: sin \: A– 3 \: cos \: A)}{(5 \: sin \: A + 3 \: cos \: A)} \\\\\\\sf \dashrightarrow \frac{[5( \frac{4}{5} ) – 3]}{[5( \frac{4}{5} ) + 3]} \\\\\\ \sf \dashrightarrow \frac{(4 - 3)}{(4 + 3)}\\\\\\ \sf \dashrightarrow \frac{1}{7}$