if four tangent A equal to 3 then 4 Sin A minus Cos A divided by 4 sin a + cos A is equal to

Question

If 4 tan A = 3 , then (4 sin A - cos A / 4 sin A + cos A) is equal to

Answer 1

Solution: We have 4tanA = 3 so, tanA = 3/4 

Now, (4sinA - cosA)/(4sinA + cosA) 

First of all divide by cosA on both LHS and RHS , 

(4sinA/cosA - cosA/cosA)/(4sinA/cosA + cosA/cosA) 

= (4tanA - 1)/(4tanA + 1)

Now, put tanA = 3/4 

= (4 × 3/4 - 1)/(4 × 3/4 + 1)

= (3 - 1)/(3 + 1) 

= 2/4 = 1/2