Question

if 5tan alpha = 4 then find the value of 5 sin alpha - 3cos alpha\ 5sin alpha + 2cos alpha = 1/6

Answer 1

In the attachment I have answered this problem.

The problem is very simple and easy
to understand.

See the attachment for detailed solution.

Answer 2

Answer:

Step-by-step explanation:

It is given that 5tanα=4⇒tanα=$\frac{4}{5}$.

Now, the value of the given expression is=$\frac{5sin{\alpha}-3cos{\alpha}}{5sin{\alpha}+2cos{\alpha}}$

=$\frac{cos{\alpha}(5\frac{sin{\alpha}}{cos{\alpha}}-3)}{cos{\alpha}(5\frac{sin{\alpha}}{cos{\alpha}}+2)}}$

=$\frac{(5\frac{sin{\alpha}}{cos{\alpha}}-3)}{(5\frac{sin{\alpha}}{cos{\alpha}}+2)}}$

=$\frac{5tan{\alpha}-3}{5tan{\alpha}+2}$

Now, putting the value of tanα=$\frac{4}{5}$,

=$\frac{4-3}{4+2}=\frac{1}{6}$

Hence proved.