Question

3tanx =4 then show that 4cosx-sinx/4cosx+sinx=4/5

Answer 1

Correct question is,

If 3 tanx = 4,

then show that,

$\dfrac{4 \cos(x) - \sin(x) }{4 \cos(x) + \sin(x) } = \dfrac{1}{2}$

Solution,

Given that

$\: \: \: \: \: \: \: \: \: \: \: 3tanx = 4 \\ \implies tanx = \frac{4}{3} \\ \implies \frac{sinx}{cosx} = \frac{4}{3} \\ \implies sinx = 4 \: \: and \: \: cosx = 3$

Now, we prove above expression as follows

LHS of given expression

$\dfrac{4cosx - sinx}{4cosx + sinx} \\ \\ = \frac{4 \times 3 - 4}{4 \times 3 + 4} \\ \\ = \frac{12- 4}{12 + 4} \\ \\ = \frac{8}{16} \\ \\ = \frac{1}{2}=RHS$

So,

LHS of given expression is equals to

RHS.

........Hence proved

Answer 2

Step-by-step explanation:

i think it is the solution