If 5tan$=4 then 5sin$-3cos$/5sin$+2cos$ is what

Question

please tell the answer with solution 

Answer 1

 

 tan = 4/5

opposite = 4

 adjacent = 5

the hypotenuse is then sqrt(41)

 

 So sin = 4/sqrt(41) = (4/41)*sqrt(41) 

      cos = 5/sqrt(41) =(5/41)*sqrt(41)

 

 

ASSUMING you mean (5 sin - 3 cos)/(5 sin + 2 cos)

 

[5 ( 4/41)*sqrt(41) - 3 ( 5/41) *Sqrt(41) ]/ [5 ( 4/41)*sqrt(41) + 2 ( 5/41) *Sqrt(41) ]

 

sqrt(41) factors out and cancels

So does (1/41)

 

(5 *4 - 3*5)/(5*4 + 2*5) = (20 - 15)/(20 + 10) = 5/30 = 1/6