Question

Plz solve this question urgent ​

Answer 1

9514 1404 393

Answer:

  2/15

Step-by-step explanation:

The given expression for θ can be rewritten to ...

  5sin(θ + arctan(-3/4)) = 0

This will have solutions ...

  θ +arctan(-3/4) = nπ

  θ = nπ - arctan(-3/4) = nπ + arctan(3/4)

__

The corresponding values of sine and cosine will be ...

  sin(arctan(3/4)) = 3/5

  cos(arctan(3/4) = 4/5

or both values may be negative. Either sign will give the same result in the expression we're to find.

  (2sin(θ) -cos(θ))/(sin(θ) +3cos(θ)) = (2(3/5) -(4/5))/(3/5 +3(4/5))

  = ((6 -4)/5)/((3+12)/5) = 2/15

  $\boxed{\dfrac{2\sin\theta-\cos\theta}{\sin\theta+3\cos\theta}=\dfrac{2}{15}}$