Question

Plz solve this question urgent ​

Answer 1

9514 1404 393

Answer:

2/15

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)

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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{(2\sin\theta-\cos\theta)/(\sin\theta+3\cos\theta)=(2)/(15)}`