Question

4 tan theta = 3

Find the value of

4 sin theta - 7 cos theta
____________________
3 sin theta - 8 sin theta

Answer 1

Answer:

= 16/15

Step-by-step explanation:

Given: 4 tan θ = 3

tan θ = opposite/adjacent= 3/4.

(i)

Here,opposite = 3 and adjacent = 4.

Hypotenuse = √3² + 4²

                    = 5.

∴ cos θ = Adjacent/Hypotenuse

            = 4/5.

(ii)

We know that sinθ = √1 - cos²θ

                               = √1 - (4/5)²

                               = √9/25

                               = 3/5.

Now,

= (4 sinθ - 7 cosθ)/(3 sinθ - 8 sinθ)

= [4(3/5) - 7(4/5)]/[3(3/5) - 8(3/5)]

= [12/5 - 28/5]/[9/5 - 24/5]

= [-16/5]/[-3]

= 16/15

Hope it helps!