Question

if 5tan alpha = 4 then find the value of 5 sin alpha - 3cos alpha \ 5sin alpha + 2cos alpha = 1/6

Answer 1

if 5 tan alpha = 4

tan alpha= 4/5

 

now

(5 sin alpha–3cos alpha) / (5 sin alpha+ 2cos alpha)

divide by cos alpha in both numerator and denominator

(5 tan alpha– 3) / (5 tan alpha + 2)

 put the value of tan alpha
(4 – 3) / (4 + 2)

 = 1/6