Question

If 4 tan theta = 3 , then find (4 sin theta - cos theta / 4 sin theta + cos theta)

Answer 1

4tanθ = 3 so, tanθ = 3/4

Now, (4sinθ - cosθ)/(4sinθ + cosθ)
First of all divide cosθ with both LHS and RHS ,
(4sinθ/cosθ - cosθ/cosθ)/(4sinθ/cosθ + cosθ/cosθ)
= (4tanθ - 1)/(4tanθ + 1)
Now, put tanθ = 3/4

= (4 × 3/4 - 1)/(4 × 3/4 + 1)
= (3 - 1)/(3 + 1)
= 2/4 = 1/2

Hence, answer is 1/2

Answer 2

4tanθ = 3 so,

tanθ = 3/4

Now, (4sinθ - cosθ)/(4sinθ + cosθ)

First of all divide cosθ with both LHS and RHS , (4sinθ/cosθ - cosθ/cosθ)/(4sinθ/cosθ + cosθ/cosθ) = (4tanθ - 1)/(4tanθ + 1)

Now, put tanθ = 3/4 = (4 × 3/4 - 1)/(4 × 3/4 + 1)

= (3 - 1)/(3 + 1)  =  2/4  =  1/2