Question

if tan theta =3/4 find the value of 4 sin theta -cos theta /4sin theta +5cos theta
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Answer 1

Step-by-step explanation:

tanθ=3/4(given)

let, opposite=3x and adjacent=4x

hence

hypotenuse=5x

hence

sin θ= opposite/hypotenuse

sin θ=3x/5x=3/5

cos θ= adjacent/hypotenuse

cos θ=4x/5x=4/5

Hence

(4sinθ-cosθ)/(4sinθ+5cosθ)

(4×3/5-4/5)/(4×3/5+5×4/5)

(8/5)/(32/5)

8/32

1/4