Question

If 5 tan theta =4 prove that 5 sin - 3 cos /5 sin +2 cos =1/6

Answer 1

5 tan theta=4
So tan theta=4/5
therefore, sin theta/cos theta = 4/5
Hence we can say that,
sin theta= 4x ,
cos theta= 5x
So,
(5 sin theta - 3 cos theta)/(5 sin theta+ 2 cos theta)
 = (20x-15x)/(20x+10x)
 = 5x/30x=1/6

Answer 2

given that 5tan theta =4
therefore sin theta / cos theta = 4/5

now
LHS = 5sin - 3cos/ 5sin +2cos
on dividing both numerator and denominator by cos... we get
( 5sin/cos - 3cos/cos)/(5sin/cos +2cos /cos)
implies ( 5*4/5 - 3*1) / (5*4/5+ 2*1)
implies (4 - 3) / (4 + 2)
which is eqal to 1/6
which is equal to RHS